Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#11759818⋊C2 |
| unambiguous semidirect product | #11759818⋊(C2×C11) |
| Fitting, socle, Hall | C11×C132 ⋊ C22×C3 |
| derived, Sylow | C132 ⋊ C22×C3×C11 |
| Hall | C11×D132 ⋊ C3 |
| Hall | C11×#92789 ⋊ C22 |
| Hall | D132 ⋊ C3×C11 |
| Hall | #92789 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #11759818⋊C2 |
| commutator, cosocle, hypocenter | C132 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 91);