Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D9×D127 |
| Fitting, Hall | C7×C9×C127 ⋊ C22 |
| derived, Hall | C9×C127 ⋊ C22×C7 |
| Hall | C7×C127 ⋊ C2×D9 |
| Sylow | C127 ⋊ C2×C7×D9 |
| Hall | C7×C9 ⋊ C2×D127 |
| Sylow | C9 ⋊ C2×C7×D127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D9×D127 |
| commutator, cosocle, hypocenter | C9×C127 | C22×C7 |
| Frattini | C3 | D3×C7×D127 |
| Fitting | C7×C9×C127 | C22 |
| socle | C3×C7×C127 | C2×D3 |
| LCS | G ▷ C9×C127 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8001 |
2730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 58);