Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
| direct product | C9×C7⋊Dic91 |
| derived, Hall | C72×C13 ⋊ C4×C9 |
| Hall | C72×C9×C13 ⋊ C4 |
| Hall | C72×C9 ⋊ Dic13 |
| Hall | C9×C13 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C9×Dic13 |
| Sylow | C13 ⋊ C9×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C7⋊D91 |
| commutator, hypocenter | C72×C13 | C4×C9 |
| Frattini | C2×C3 | C3×C7⋊D91 |
| Fitting | C2×C72×C9×C13 | C2 |
| socle, prime radical, cosocle | C2×C3×C72×C13 | C2×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2×C9 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22932 |
5760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 337);