Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #3861×Dic39 |
| unambiguous semidirect product | C3⋊(Dic13×#3861) |
| derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×C13×#3861 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C3×#3861 ⋊ Dic13 |
| Sylow | C72 ⋊ C3×Dic39 |
| Sylow | C13 ⋊ Dic3×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D39×#3861 |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×C13×#3861 | C2 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7644 |
798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 744);