Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C9×C127 ⋊ C22×C7 |
| Hall | C9×C127⋊C7 ⋊ C22 |
| Hall | D9×D127 ⋊ C7 |
| Hall | C127⋊C7 ⋊ C2×D9 |
| Sylow | C127 ⋊ C2×C7×D9 |
| Sylow | C9 ⋊ C2×D127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C127 | C22×C7 |
| Frattini | C3 | D3×D127⋊C7 |
| socle | C3×C127 | C2×D3×C7 |
| LCS | G ▷ C9×C127 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1143 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 33);