Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C127⋊C3)⋊Dic7 |
| unambiguous semidirect product | (C127⋊C3)⋊(C3×Dic7) |
| derived, Hall | C7×C127 ⋊ C32×C4 |
| Hall | C3×C7×C127⋊C3 ⋊ C4 |
| Hall | Dic889 ⋊ C32 |
| Hall | C3×C127⋊C3 ⋊ Dic7 |
| Sylow | C127 ⋊ C32×Dic7 |
| Sylow | C7 ⋊ C3×(C127⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 119);