Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×C22⋊#89204 |
| unambiguous semidirect product | C22⋊(C13×#89204) |
| derived, Hall | C22×C72 ⋊ C9×C13 |
| Hall | C22×C72×C13 ⋊ C9 |
| Hall | C72×C13 ⋊ C22⋊C9 |
| Hall | C22×C13 ⋊ #89204 |
| Sylow | C72 ⋊ C13×C22⋊C9 |
| Sylow | C22 ⋊ C13×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C22⋊#3861 |
| commutator, hypocenter | C22×C72 | C9×C13 |
| Frattini | C3 | C13×C22⋊#3861 |
| Fitting, socle, prime radical | C22×C3×C72×C13 | C3 |
| cosocle | C22×C3×C72 | C3×C13 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C3×C13 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11466 |
2652 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 546);