Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#14523128 |
| derived, Hall | C11×C132 ⋊ C3×C4 |
| Hall | C11⋊#10621725 ⋊ C3 |
| Hall | C11×#92788 ⋊ C4 |
| Hall | #92788 ⋊ Dic11 |
| Sylow | C132 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ #14523128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#11759815 |
| commutator, hypocenter | C11×C132 | C3×C4 |
| Fitting, socle, cosocle | C2×C11×C132 | C2×C3 |
| prime radical | C2×C11×#92788 | C2 |
| LCS | G ▷ C11×C132 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7436 |
Polycyclic presentation:
2,3,11,13^2,2|a^2=f,c^a=c^10,d^a=d^12,e^a=e^12,d^b=d^3,e^b=e^3658 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 52);