Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C3 |
| direct product | C49×#90866 |
| Fitting, Hall | C32×C13×C49 ⋊ C4 |
| derived, Hall | C32×C13 ⋊ C4×C49 |
| Hall | C13×C49 ⋊ #157 |
| Hall | C32×C49 ⋊ #261 |
| Sylow | C13 ⋊ #157×C49 |
| Sylow | C32 ⋊ C49×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #90866 |
| commutator, hypocenter | C32×C13 | C4×C49 |
| Frattini | C7 | C7×#90866 |
| Fitting | C32×C13×C49 | C4 |
| socle | C32×C7×C13 | C4×C7 |
| prime radical, cosocle | C7×C3⋊D39 | C2×C7 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C49 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3822 |
1617 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 243);