Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C127 · Schur multiplier (H2) = C1 |
| direct product | C127×C3⋊(ΓL(1,𝔽8)⋊C4) |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)⋊C4×C127) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(Dic3×C127) |
| unambiguous semidirect product | Dic21⋊(C3×C127) |
| derived | C3×C7 ⋊ C3×C4×C127 |
| Hall | C3×ΓL(1,𝔽8)×C127 ⋊ C4 |
| Hall | C7×C127 ⋊ C3×Dic3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C4×C127 |
| Sylow | C7 ⋊ C3×Dic3×C127 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
3048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 123);