Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C127 · Schur multiplier (H2) = C2 |
| direct product | D7×D9×C127 |
| unambiguous semidirect product | (C7×D9)⋊(C2×C127) |
| unambiguous semidirect product | (C9×D7)⋊(C2×C127) |
| unambiguous semidirect product | D63⋊(C2×C127) |
| Fitting, Hall | C7×C9×C127 ⋊ C22 |
| derived, Hall | C7×C9 ⋊ C22×C127 |
| Hall | C9×C127 ⋊ C2×D7 |
| Hall | C7×C127 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D7×C127 |
| Sylow | C7 ⋊ C2×D9×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | D7×D9 |
| commutator, cosocle, hypocenter | C7×C9 | C22×C127 |
| Frattini | C3 | D3×D7×C127 |
| Fitting | C7×C9×C127 | C22 |
| socle | C3×C7×C127 | C2×D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C127 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8001 |
3810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 60);