Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D9×C127⋊C7 |
| unambiguous semidirect product | C9⋊(C22×C127⋊C7) |
| unambiguous semidirect product | (C2×C9)⋊(C2×C127⋊C7) |
| unambiguous semidirect product | (C2×D9×C127)⋊C7 |
| Fitting | C2×C9×C127 ⋊ C2×C7 |
| derived, Hall | C9×C127 ⋊ C22×C7 |
| Hall | C9×C127⋊C7 ⋊ C22 |
| Hall | C2×D9×C127 ⋊ C7 |
| Sylow | C127 ⋊ C2×C7×D9 |
| Sylow | C9 ⋊ C22×C127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C127⋊C7 |
| commutator, cosocle, hypocenter | C9×C127 | C22×C7 |
| Frattini | C3 | C2×D3×C127⋊C7 |
| Fitting | C2×C9×C127 | C2×C7 |
| socle | C2×C3×C127 | D3×C7 |
| LCS | G ▷ C9×C127 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2286 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 39);