Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C13 |
| direct product | C11×#14523161 |
| Fitting, socle, Hall | C11×C132 ⋊ Dic3 |
| derived, Hall | #92789 ⋊ C4×C11 |
| Hall | C11×#92789 ⋊ C4 |
| Sylow | C132 ⋊ C11×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #14523161 |
| commutator, hypocenter | #92789 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C132 | Dic3 |
| prime radical | C11×#11759816 | C2 |
| cosocle | #11759816 | C2×C11 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 77);