Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×C3⋊(C7⋊(C7⋊#261)) |
| unambiguous semidirect product | C3⋊(C3×C7⋊(C7⋊#261)) |
| Fitting, socle, Hall | C32×C72×C13 ⋊ C4 |
| derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C32×C72 ⋊ #261 |
| Hall | C32×C13 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C3×C3⋊#261 |
| Sylow | C13 ⋊ C3×C3⋊(C7⋊Dic7) |
| Sylow | C32 ⋊ C7⋊(C7⋊#261) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C7⋊(C7⋊#261)) |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C13 | C4 |
| prime radical | C32×C72×D13 | C2 |
| cosocle | C3×C72×D13 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 ◁ C3 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3822 |
1773 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1541);