Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11×C13 · Schur multiplier (H2) = C2 |
| direct product | C22×C11×C13×C13⋊C3 |
| Fitting, socle, Hall | C22×C11×C132 ⋊ C3 |
| derived | C13 ⋊ C22×C3×C11×C13 |
| Hall | C11×C132 ⋊ C22×C3 |
| Hall | C22×C132 ⋊ C3×C11 |
| Sylow | C132 ⋊ C22×C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C11×C13 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C22×C3×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C132 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C11×C13 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1716 |
4004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 189);