Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D169 |
| unambiguous semidirect product | D507⋊D11 |
| unambiguous semidirect product | D1859⋊D3 |
| Fitting, derived, Hall | C3×C11×C169 ⋊ C22 |
| Hall | C11×C169 ⋊ C2×D3 |
| Hall | C3×C169 ⋊ C2×D11 |
| Sylow | C169 ⋊ D3×D11 |
| Hall | C3×C11 ⋊ C2×D169 |
| Sylow | C11 ⋊ D3×D169 |
| Sylow | C3 ⋊ D11×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C11×C169 | C22 |
| Frattini | C13 | D33⋊D13 |
| socle | C3×C11×C13 | C2×D13 |
| LCS | G ▷ C3×C11×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5577 |
Polycyclic presentation:
2^2,3,11,13^2|e^13=f^12,d^a=d^10,e^a=e^12f,f^a=f^12,c^b=c^2,d^b=d^101533 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 30);