Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11759813⋊D11 |
| Fitting, socle, Hall | C11×C132 ⋊ C2×D3 |
| derived, Hall | C11×#92789 ⋊ C22 |
| Hall | #92789 ⋊ C2×D11 |
| Sylow | C132 ⋊ D3×D11 |
| Sylow | C11 ⋊ #11759813⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×#92789 | C22 |
| Fitting, socle | C11×C132 | C2×D3 |
| LCS | G ▷ C11×#92789 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2^2,3,11,13^2|c^a=c^2,d^a=d^10,e^a=f,f^a=e,c^b=c^2,e^b=f^12,f^b=e^12,e^c=e^3,f^c=f^9283 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 95);