===== surfaces-register =====

FIELDS: (a=1,p=5), $k=\QQ$, $\ell=\QQ[i]$
 DETERMINANT:  $\det(x)=D(x)$, a power of $(3+4i)/5$, modulo cubes
 CLASS: (a=1,p=5,\emptyset)

   FPP/3: (a=1,p=5,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C4 x C3
     FUNDAMENTAL GROUP:  C2 x C4
     FIRST HOMOLOGY:     C2 x C4
     COVERED BY: (a=1,p=5,\emptyset,D_3) index 3, regular
                 (a=1,p=5,\{2I\})        index 3, not regular

   FPP: (a=1,p=5,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C4 x C31
     COVERS: (a=1,p=5,\emptyset) index 3, regular

 CLASS: (a=1,p=5,\{2\})

   FPP/3: (a=1,p=5,\{2\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C4 x C3
     FUNDAMENTAL GROUP:  C4
     FIRST HOMOLOGY:     C4
     COVERED BY: (a=1,p=5,\{2\},D_3) index 3, regular
                 (a=1,p=5,\{2I\})    index 3, not regular

   FPP: (a=1,p=5,\{2\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C4 x C31
     COVERS: (a=1,p=5,\{2\}) index 3, regular

 CLASS: (a=1,p=5,\{2I\})

   FPP: (a=1,p=5,\{2I\})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C4 x C4 x C3
     COVERS: (a=1,p=5,\emptyset) index 3, not regular
             (a=1,p=5,\{2\})     index 3, not regular


 FIELDS: (a=2,p=3), $k=\QQ$, $\ell=\QQ[\sqrt{-2}]$
 DETERMINANT:  $\det(x)=D(x)$, a power of $(1+2\sqrt{-2})/3$, modulo cubes
 CLASS: (a=2,p=3,\emptyset)

   FPP/3: (a=2,p=3,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  C2 x C2
     FIRST HOMOLOGY:     C2 x C2
     COVERED BY: (a=2,p=3,\emptyset,D_3) index 3, regular
                 (a=2,p=3,\{2I\})        index 3, not regular

   FPP: (a=2,p=3,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C2 x C13
     COVERS: (a=2,p=3,\emptyset) index 3, regular

 CLASS: (a=2,p=3,\{2\})

   FPP/3: (a=2,p=3,\{2\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  C2 x C2
     FIRST HOMOLOGY:     C2 x C2
     COVERED BY: (a=2,p=3,\{2\},D_3) index 3, regular
                 (a=2,p=3,\{2I\})    index 3, not regular

   FPP: (a=2,p=3,\{2\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C2 x C13
     COVERS: (a=2,p=3,\{2\}) index 3, regular

 CLASS: (a=2,p=3,\{2I\})

   FPP: (a=2,p=3,\{2I\})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C2 x C2 x C3
     COVERS: (a=2,p=3,\emptyset) index 3, not regular
             (a=2,p=3,\{2\})     index 3, not regular

 FIELDS: (a=7,p=2), $k=\QQ$, $\ell=\QQ[\sqrt{-7}]$
 DETERMINANT:  $\det(x)=D(x)$, a power of $(3+\sqrt{-7})/4$, modulo cubes

 CLASS: (a=7,p=2,\emptyset)

   FPP/21: (a=7,p=2,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (a=7,p=2,\emptyset,D_3)      index 3, regular
                 (a=7,p=2,\emptyset,2_7)      index 7, not regular
                 (a=7,p=2,\emptyset,X_7)      index 7, not regular
                 (a=7,p=2,\emptyset,D_3 2_7)  index 21, regular
                 (a=7,p=2,\emptyset,7_{21})   index 21, not regular
                 (a=7,p=2,\emptyset,D_3 X_7)  index 21, not regular

   FPP/7: (a=7,p=2,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C2 x C7
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (a=7,p=2,\emptyset,D_3 2_7) index 7, regular
                 (a=7,p=2,\emptyset,D_3 X_7) index 7, not regular
     COVERS:     (a=7,p=2,\emptyset)         index 3, regular

    FPP/3: (a=7,p=2,\emptyset,2_7)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  D8
     FIRST HOMOLOGY:     C2 x C2
     COVERED BY: (a=7,p=2,\emptyset,D_3 2_7) index 3, regular
     COVERS:     (a=7,p=2,\emptyset)         index 7, not regular

   FPP/3: (a=7,p=2,\emptyset,X_7)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (a=7,p=2,\emptyset,D_3 X_7) index 3, regular
     COVERS:     (a=7,p=2,\emptyset)         index 7, not regular

   FPP: (a=7,p=2,\emptyset,D_3 2_7)
     AUTOMORPHISM GROUP: C7 : C3
     FIRST HOMOLOGY:     C2^4
     COVERS: (a=7,p=2,\emptyset)     index 21, regular
             (a=7,p=2,\emptyset,D_3) index 7, regular
             (a=7,p=2,\emptyset,2_7) index 3, regular

   FPP: (a=7,p=2,\emptyset,7_{21})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C3 x C7
     COVERS: (a=7,p=2,\emptyset) index 21, not regular

   FPP: (a=7,p=2,\emptyset,D_3 X_7)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C7
     COVERS: (a=7,p=2,\emptyset)     index 21, not regular
             (a=7,p=2,\emptyset,D_3) index 7, not regular
             (a=7,p=2,\emptyset,X_7) index 3, regular

  CLASS: (a=7,p=2,\{7\})

   FPP/21: (a=7,p=2,\{7\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     COVERED BY: (a=7,p=2,\{7\},D_3)      index 3, regular
                 (a=7,p=2,\{7\},2_7)      index 7, not regular
                 (a=7,p=2,\{7\},7_7)      index 7, not regular
                 (a=7,p=2,\{7\},7'_7)     index 7, not regular
                 (a=7,p=2,\{7\},D_3 2_7)  index 21, regular
                 (a=7,p=2,\{7\},D_3 7_7)  index 21, not regular
                 (a=7,p=2,\{7\},D_3 7'_7) index 21, not regular
                 (a=7,p=2,\{7\},7_{21})   index 21, not regular


   FPP/7: (a=7,p=2,\{7\},D_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C7
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     COVERED BY: (a=7,p=2,\{7\},D_3 2_7)  index 7, regular
                 (a=7,p=2,\{7\},D_3 7_7)  index 7, not regular
                 (a=7,p=2,\{7\},D_3 7'_7) index 7, not regular
     COVERS:     (a=7,p=2,\{7\})          index 3, regular

    FPP/3: (a=7,p=2,\{7\},2_7)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (a=7,p=2,\{7\},D_3 2_7) index 3, regular
     COVERS:     (a=7,p=2,\{7\})         index 7, not regular

   FPP/3: (a=7,p=2,\{7\},7_7)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (a=7,p=2,\{7\},D_3 7_7) index 3, regular
                 (a=7,p=2,\{7\},7_{21})  index 3, not regular
     COVERS:     (a=7,p=2,\{7\})         index 7, not regular


   FPP/3: (a=7,p=2,\{7\},7'_7)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  C2 x C2
     FIRST HOMOLOGY:     C2 x C2
     COVERED BY: (a=7,p=2,\{7\},D_3 7'_7) index 3, regular
                 (a=7,p=2,\{7\},7_{21})   index 3, not regular
     COVERS:     (a=7,p=2,\{7\})          index 7, not regular

   FPP: (a=7,p=2,\{7\},D_3 2_7)
     AUTOMORPHISM GROUP: C7 : C3
     FIRST HOMOLOGY:     C2 x C2 x C2
     COVERS: (a=7,p=2,\{7\})     index 21, regular
             (a=7,p=2,\{7\},D_3) index 7, regular
             (a=7,p=2,\{7\},2_7) index 3, regular

   FPP: (a=7,p=2,\{7\},D_3 7_7)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C7
     COVERS: (a=7,p=2,\{7\})     index 21, not regular
             (a=7,p=2,\{7\},D_3) index 7, not regular
             (a=7,p=2,\{7\},7_7) index 3, regular

   FPP: (a=7,p=2,\{7\},D_3 7'_7})
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2  x C2 x C7
     COVERS: (a=7,p=2,\{7\})      index 21, not regular
             (a=7,p=2,\{7\},D_3)  index 7, not regular
             (a=7,p=2,\{7\},7'_7) index 3, regular

   FPP: (a=7,p=2,\{7\},7_{21})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C2 x C3
     COVERS: (a=7,p=2,\{7\})      index 21, not regular
             (a=7,p=2,\{7\},7_7)  index 3, not regular
             (a=7,p=2,\{7\},7'_7) index 3, not regular

  CLASS: (a=7,p=2,\{3\})

   FPP/3: (a=7,p=2,\{3\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C4 x C3
     FUNDAMENTAL GROUP:  C2 x C4
     FIRST HOMOLOGY:     C2 x C4
     COVERED BY: (a=7,p=2,\{3\},D_3) index 3, regular
                 (a=7,p=2,\{3\},3_3) index 3, not regular

   FPP: (a=7,p=2,\{3\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C4 x C7
     COVERS: (a=7,p=2,\{3\}) index 3, regular

   FPP: (a=7,p=2,\{3\},3_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C4 x C3
     COVERS: (a=7,p=2,\{3\}) index 3, not regular

 CLASS: (a=7,p=2,\{3,7\})

   FPP/3: (a=7,p=2,\{3,7\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3 x C4
     FUNDAMENTAL GROUP:  C4
     FIRST HOMOLOGY:     C4
     COVERED BY: (a=7,p=2,\{3,7\},D_3) index 3, regular
                 (a=7,p=2,\{3,7\},3_3) index 3, not regular

   FPP: (a=7,p=2,\{3,7\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C4 x C7
     COVERS: (a=7,p=2,\{3,7\}) index 3, regular

   FPP: (a=7,p=2,\{3,7\},3_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C4 x C3
     COVERS: (a=7,p=2,\{3,7\}) index 3, not regular

  CLASS: (a=7,p=2,\{5\})

   FPP: (a=7,p=2,\{5\})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C9

 CLASS: (a=7,p=2,\{5,7\})

   FPP: (a=7,p=2,\{5,7\})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C9

FIELDS: (a=15,p=2), $k=\QQ$, $\ell=\QQ[\sqrt{-15}]$
 DETERMINANT:  $\det(x)=D(x)$, a power of $(1+\sqrt{-15)/4$, modulo cubes

  CLASS: (a=15,p=2,\emptyset)

   FPP/3: (a=15,p=2,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  C2 x C2
     FIRST HOMOLOGY:     C2 x C2
     COVERED BY: (a=15,p=2,\emptyset,D_3) index 3, regular
                 (a=15,p=2,\emptyset,3_3) index 3, not regular

   FPP: (a=15,p=2,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C2 x C7
     COVERS: (a=15,p=2,\emptyset) index 3, regular

   FPP: (a=15,p=2,\emptyset,3_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C2 x C9
     COVERS: (a=15,p=2,\emptyset) index 3, not regular

  CLASS: (a=15,p=2,\{3\})

   FPP/3: (a=15,p=2,\{3\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3 x C3
     FUNDAMENTAL GROUP:  C2 x C3
     FIRST HOMOLOGY:     C2 x C3
     COVERED BY: (a=15,p=2,\{3\},D_3)    index 3, regular
                 (a=15,p=2,\{3\},3_3)    index 3, regular
                 (a=15,p=2,\{3\},(D3)_3) index 3, regular

   FPP: (a=15,p=2,\{3\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C3 x C7
     COVERS: (a=15,p=2,\{3\}) index 3, regular

   FPP: (a=15,p=2,\{3\},3_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C2 x C2 x C3
     COVERS: (a=15,p=2,\{3\}) index 3, regular

   FPP: (a=15,p=2,\{3\},(D3)_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C3
     COVERS: (a=15,p=2,\{3\}) index 3, regular

 CLASS: (a=15,p=2,\{5\})

   FPP/3: (a=15,p=2,\{5\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (a=15,p=2,\{5\},D_3) index 3, regular
                 (a=15,p=2,\{5\},3_3) index 3, not regular

   FPP: (a=15,p=2,\{5\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C7
     COVERS: (a=15,p=2,\{5\}) index 3, regular

   FPP: (a=15,p=2,\{5\},3_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C2 x C9
     COVERS: (a=15,p=2,\{5\}) index 3, not regular

  CLASS: (a=15,p=2,\{3,5\})

   FPP/3: (a=15,p=2,\{3,5\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3 x C3
     FUNDAMENTAL GROUP:  C3
     FIRST HOMOLOGY:     C3
     COVERED BY: (a=15,p=2,\{3,5\},D_3)    index 3, regular
                 (a=15,p=2,\{3,5\},3_3)    index 3, regular
                 (a=15,p=2,\{3,5\},(D3)_3) index 3, regular

   FPP: (a=15,p=2,\{3,5\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C3 x C7
     COVERS: (a=15,p=2,\{3,5\}) index 3, regular

   FPP: (a=15,p=2,\{3,5\},3_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C2 x C3
     COVERS: (a=15,p=2,\{3,5\}) index 3, regular

   FPP: (a=15,p=2,\{3,5\},(D3)_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C3
     COVERS: (a=15,p=2,\{3,5\}) index 3, regular

FIELDS: (a=23,p=2), $k=\QQ$, $\ell=\QQ[\sqrt{-23}]$
 DETERMINANT:  $\det(x)=D(x)$, a power of $(7+3\sqrt{-23)/16$, modulo cubes

 CLASS: (a=23,p=2,\emptyset)

   FPP: (a=23,p=2,\emptyset)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C3 x C7

 CLASS: (a=23,p=2,\{23\})

   FPP: (a=23,p=2,\{23\})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C3 x C7

 FIELDS: (C2,p=2), $k=\QQ[\sqrt{5}]$, $\ell=k[\sqrt{-3}]$
 DETERMINANT:  $\det(x)=d(x)D(x)$ with
   $d(x)$ a power of $\zeta_3$
   $D(x)$ a power of $(1+\sqrt{-15})/4$, modulo cubes

 CLASS: (C2,p=2,\emptyset)

   FPP/9: (C2,p=2,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     NO LIFT TO SU(2,1)
     COVERED BY: (C2,p=2,\emptyset,D_3)          index 3, regular
                 (C2,p=2,\emptyset,d_3)          index 3, regular
                 (C2,p=2,\emptyset,(dD)_3)       index 3, regular
                 (C2,p=2,\emptyset,(d^2D)_3)     index 3, regular
                 (C2,p=2,\emptyset,X_3)          index 3, not regular

                 (C2,p=2,\emptyset,d_3 D_3)      index 9, regular
                 (C2,p=2,\emptyset,D_3 X_3)      index 9, not regular
                 (C2,p=2,\emptyset,(dD)_3 X_3)   index 9, not regular
                 (C2,p=2,\emptyset,(d^2D)_3 X_3) index 9, not regular
                 (C2,p=2,\emptyset,d_3 X'_3)     index 9, not regular
                 (C2,p=2,\emptyset,X_9)          index 9, not regular

    FPP/3: (C2,p=2,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C2 x C3 x C7
     FUNDAMENTAL GROUP:  C2 x C7
     FIRST HOMOLOGY:     C2 x C7
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\emptyset,d_3 D_3) index 3, regular
                 (C2,p=2,\emptyset,D_3 X_3) index 3, not regular
     COVERS:     (C2,p=2,\emptyset)         index 3, regular

   FPP/3: (C2,p=2,\emptyset,d_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  S3
     FIRST HOMOLOGY:     C2
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\emptyset,d_3 D_3)  index 3, regular
                 (C2,p=2,\emptyset,d_3 X'_3) index 3, not regular
     COVERS:     (C2,p=2,\emptyset)          index 3, regular

   FPP/3: (C2,p=2,\emptyset,(dD)_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\emptyset,d_3 D_3)    index 3, regular
                 (C2,p=2,\emptyset,(dD)_3 X_3) index 3, not regular
     COVERS:     (C2,p=2,\emptyset)            index 3, regular

   FPP/3: (C2,p=2,\emptyset,(d^2D)_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\emptyset,d_3 D_3)      index 3, regular
                 (C2,p=2,\emptyset,(d^2D)_3 X_3) index 3, not regular
     COVERS:     (C2,p=2,\emptyset)              index 3, regular

   FPP/3: (C2,p=2,\emptyset,X_3)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3 x C3
     FUNDAMENTAL GROUP:  C2 x C3
     FIRST HOMOLOGY:     C2 x C3
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\emptyset,D_3 X_3)      index 3, regular
                 (C2,p=2,\emptyset,(dD)_3 X_3)   index 3, regular
                 (C2,p=2,\emptyset,(d^2D)_3 X_3) index 3, regular
                 (C2,p=2,\emptyset,X_9)          index 3, not regular
     COVERS:     (C2,p=2,\emptyset)              index 3, not regular

    FPP: (C2,p=2,\emptyset,d_3 D_3)
     AUTOMORPHISM GROUP: C3 x C3
     FIRST HOMOLOGY:     C2 x C7
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\emptyset)          index 9, regular
             (C2,p=2,\emptyset,d_3)      index 3, regular
             (C2,p=2,\emptyset,D_3)      index 3, regular
             (C2,p=2,\emptyset,(dD)_3)   index 3, regular
             (C2,p=2,\emptyset,(d^2D)_3) index 3, regular

   FPP: (C2,p=2,\emptyset,D_3 X_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C9 x C7
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\emptyset)     index 9, not regular
             (C2,p=2,\emptyset,D_3) index 3, not regular
             (C2,p=2,\emptyset,X_3) index 3, regular

   FPP: (C2,p=2,\emptyset,(dD)_3 X_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C9
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\emptyset)        index 9, not regular
             (C2,p=2,\emptyset,(dD)_3) index 3, not regular
             (C2,p=2,\emptyset,X_3)    index 3, regular

   FPP: (C2,p=2,\emptyset,(d^2D)_3 X_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C9
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\emptyset)          index 9, not regular
             (C2,p=2,\emptyset,(d^2D)_3) index 3, not regular
             (C2,p=2,\emptyset,X_3)      index 3, regular

   FPP: (C2,p=2,\emptyset,d_3 X'_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C3 x C3
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\emptyset)     index 9, not regular
             (C2,p=2,\emptyset,d_3) index 3, not regular

   FPP: (C2,p=2,\emptyset,X_9)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C3 x C3
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\emptyset)     index 9, not regular
             (C2,p=2,\emptyset,X_3) index 3, not regular

  CLASS: (C2,p=2,\{3\})

   FPP/9: (C2,p=2,\{3\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3 x C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     NO LIFT TO SU(2,1)
     COVERED BY: (C2,p=2,\{3\},D_3)      index 3, regular
                 (C2,p=2,\{3\},d_3)      index 3, regular
                 (C2,p=2,\{3\},(dD)_3)   index 3, regular
                 (C2,p=2,\{3\},(d^2D)_3) index 3, regular

                 (C2,p=2,\{3\},d_3 D_3)  index 9, regular

   FPP/3: (C2,p=2,\{3\},D_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3 x C7
     FUNDAMENTAL GROUP:  C7
     FIRST HOMOLOGY:     C7
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\{3\},d_3 D_3) index 3, regular
     COVERS:     (C2,p=2,\{3\})         index 3, regular

   FPP/3: (C2,p=2,\{3\},d_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\{3\},d_3 D_3) index 3, regular
     COVERS:     (C2,p=2,\{3\})         index 3, regular

   FPP/3: (C2,p=2,\{3\},(dD)_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\{3\},d_3 D_3) index 3, regular
     COVERS:     (C2,p=2,\{3\})         index 3, regular

   FPP/3: (C2,p=2,\{3\},(d^2D)_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     LIFTS TO SU(2,1)
     COVERED BY: (C2,p=2,\{3\},d_3 D_3) index 3, regular
     COVERS:     (C2,p=2,\{3\})         index 3, regular

    FPP: (C2,p=2,\{3\},d_3 D_3)
     AUTOMORPHISM GROUP: C3 x C3
     FIRST HOMOLOGY:     C7
     LIFTS TO SU(2,1)
     COVERS: (C2,p=2,\{3\})          index 9, regular
             (C2,p=2,\{3\},d_3)      index 3, regular
             (C2,p=2,\{3\},D_3)      index 3, regular
             (C2,p=2,\{3\},(dD)_3)   index 3, regular
             (C2,p=2,\{3\},(d^2D)_3) index 3, regular

FIELDS: (C10,p=2), $k=\QQ[\sqrt{2}]$, $\ell=k[\sqrt{-5+2\sqrt{2}}]$
 DETERMINANT:  $\det(x)=D(x)$, a power of
   $((1+\sqrt{2})+\sqrt{-5+2\sqrt{2}})/(2\sqrt{2})$, modulo cubes

 CLASS: (C10,p=2,\emptyset)

   FPP/3: (C10,p=2,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3
     FUNDAMENTAL GROUP:  C2
     FIRST HOMOLOGY:     C2
     COVERED BY: (C10,p=2,\emptyset,D_3) index 3, regular

   FPP: (C10,p=2,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C7
     COVERS: (C10,p=2,\emptyset) index 3, regular

 CLASS: (C10,p=2,\{17-})

   FPP/3: (C10,p=2,\{17-\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     COVERED BY: (C10,p=2,\{17-\},D_3) index 3, regular

   FPP: (C10,p=2,\{17-\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C7
     COVERS: (C10,p=2,\{17-\}) index 3, regulrar

 FIELDS: (C18,p=3), $k=\QQ[\sqrt{6}]$, $\ell=k[\sqrt{-3}]$
 DETERMINANT:  $\det(x)=d(x)D(x)$ with
   $d(x)$ a power of $\zeta_3$
   $D(x)$ a power of $(\sqrt{6}+\sqrt{-3})/3$, modulo cubes
 
 CLASS: (C18,p=3,\emptyset)

   FPP/9: (C18,p=3,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3 x C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     NO LIFT TO SU(2,1)
     COVERED BY: (C18,p=3,\emptyset,D_3)      index 3, regular
                 (C18,p=3,\emptyset,d_3)      index 3, regular
                 (C18,p=3,\emptyset,(dD)_3)   index 3, regular
                 (C18,p=3,\emptyset,(d^2D)_3) index 3, regular
                 (C18,p=3,\emptyset,d_3 D_3)  index 9, regular
                 (C18,p=3,\{2I})              index 9, not regular

    FPP/3: (C18,p=3,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3 x C13
     FUNDAMENTAL GROUP:  C13
     FIRST HOMOLOGY:     C13
     LIFTS TO SU(2,1)
     COVERS:     (C18,p=3,\emptyset)        index 3, regular
     COVERED BY: (C18,p=3,\emptyset,d_3D_3) index 3, regular

   FPP/3: (C18,p=3,\emptyset,d_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  Q8
     FIRST HOMOLOGY:     C2 x C2
     LIFTS TO SU(2,1)
     COVERS:     (C18,p=3,\emptyset)         index 3, regular
     COVERED BY: (C18,p=3,\emptyset,d_3 D_3) index 3, regular

   FPP/3: (C18,p=3,\emptyset,(dD)_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     LIFTS TO SU(2,1)
     COVERS:     (C18,p=3,\emptyset)         index 3, regular
     COVERED BY: (C18,p=3,\emptyset,d_3 D_3) index 3, regular

   FPP/3: (C18,p=3,\emptyset,(d^2D)_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     LIFTS TO SU(2,1)
     COVERS:     (C18,p=3,\emptyset)         index 3, regular
     COVERED BY: (C18,p=3,\emptyset,d_3 D_3) index 3, regular

   FPP: (C18,p=3,\emptyset,d_3 D_3)
     AUTOMORPHISM GROUP: C3 x C3
     FIRST HOMOLOGY:     C2 x C2 x C13
     LIFTS TO SU(2,1)
     COVERS: (C18,p=3,\emptyset)          index 9, regular
             (C18,p=3,\emptyset,D_3)      index 3, regular
             (C18,p=3,\emptyset,d_3)      index 3, regular
             (C18,p=3,\emptyset,(dD)_3)   index 3, regular
             (C18,p=3,\emptyset,(d^2D)_3) index 3, regular

  CLASS: (C18,p=3,\{2\})

   FPP/3: (C18,p=3,\{2\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C3 x C3
     FUNDAMENTAL GROUP:  C2 x C3
     FIRST HOMOLOGY:     C2 x C3
     NO LIFT TO SU(2,1)
     COVERED BY: (C18,p=3,\{2\},D_3)      index 3, regular
                 (C18,p=3,\{2\},(dD)_3)   index 3, regular
                 (C18,p=3,\{2\},(d^2D)_3) index 3, regular
                 (C18,p=3,\{2I\})         index 3, not regular

   FPP: (C18,p=3,\{2\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C3 x C13
     NO LIFT TO SU(2,1)
     COVERS: (C18,p=3,\{2\}) index 3, regular

   FPP: (C18,p=3,\{2\},(dD)_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C3
     NO LIFT TO SU(2,1)
     COVERS: (C18,p=3,\{2\}) index 3, regular

   FPP: (C18,p=3,\{2\},(d^2D)_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C2 x C3
     NO LIFT TO SU(2,1)
     COVERS: (C18,p=3,\{2\}) index 3, regular

 CLASS: (C18,p=3,\{2I\})

   FPP: (C18,p=3,\{2I\})
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C3 x C3
     NO LIFT TO SU(2,1)
     COVERS: (C18,p=3,\emptyset) index 9, not regular
             (C18,p=3,\{2\})     index 3, not regular

 FIELDS: (C20,p=2), $k=\QQ[\sqrt{7}]$, $\ell=k[i]$
 DETERMINANT:  $\det(x)=D(x)$, a power of $(3+\sqrt{-7})/4$, modulo
   cubes

 CLASS: (C20,p=2,\emptyset)

   FPP/21: (C20,p=2,\emptyset)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C3
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     COVERED BY: (C20,p=2,\emptyset,D_3)     index 3, regular
                 (C20,p=2,\emptyset,2_7)     index 7, not regular
                 (C20,p=2,\emptyset,D_3 2_7) index 21, regular

   FPP/7: (C20,p=2,\emptyset,D_3)
     AUTOMORPHISM GROUP: C3
     ABELIANIZATION:     C7
     FUNDAMENTAL GROUP:  trivial
     FIRST HOMOLOGY:     trivial
     COVERED BY: (C20,p=2,\emptyset,D_3 2_7) index 7, regular
     COVERS:     (C20,p=2,\emptyset)         index 3, regular

   FPP/3: (C20,p=2,\emptyset,2_7)
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C2 x C2 x C3
     FUNDAMENTAL GROUP:  C2 x C2
     FIRST HOMOLOGY:     C2 x C2
     COVERED BY: (C20,p=2,\emptyset,D_3 2_7) index 3, regular
     COVERS:     (C20,p=2,\emptyset)         index 7, not regular

   FPP: (C20,p=2,\emptyset,D_3 2_7)
     AUTOMORPHISM GROUP: C7 : C3
     FIRST HOMOLOGY:     C2^6
     COVERS: (C20,p=2,\emptyset)     index 21, regular
             (C20,p=2,\emptyset,D_3) index 7, regular
             (C20,p=2,\emptyset,2_7) index 3, regular

  CLASS: (C20,p=2,\{3+\})

   FPP/3: (C20,p=2,\{3+\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C4 x C3
     FUNDAMENTAL GROUP:  C4
     FIRST HOMOLOGY:     C4
     COVERED BY: (C20,p=2,\{3+\},D_3)    index 3, regular
                 (C20,p=2,\{3+\},{3+}_3) index 3, not regular

   FPP: (C20,p=2,\{3+\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C4 x C7
     COVERS: (C20,p=2,\{3+\}) index 3, regular

   FPP: (C20,p=2,\{3+\},{3+}_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C4 x C3
     COVERS: (C20,p=2,\{3+\}) index 3, not regular

 CLASS: (C20,p=2,\{3-\})

   FPP/3: (C20,p=2,\{3-\})
     AUTOMORPHISM GROUP: trivial
     ABELIANIZATION:     C4 x C3
     FUNDAMENTAL GROUP:  C4
     FIRST HOMOLOGY:     C4
     COVERED BY: (C20,p=2,\{3-\},D_3)    index 3, regular
                 (C20,p=2,\{3-\},{3-}_3) index 3, not regular

   FPP: (C20,p=2,\{3-\},D_3)
     AUTOMORPHISM GROUP: C3
     FIRST HOMOLOGY:     C4 x C7
     COVERS: (C20,p=2,\{3-\}) index 3, regular

   FPP: (C20,p=2,\{3-\},{3-}_3)
     AUTOMORPHISM GROUP: trivial
     FIRST HOMOLOGY:     C2 x C4 x C3
     COVERS: (C20,p=2,\{3-\}) index 3, not regular