Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C11×D169 |
| unambiguous semidirect product | (D3×C169)⋊(C2×C11) |
| unambiguous semidirect product | (C3×D169)⋊(C2×C11) |
| unambiguous semidirect product | D507⋊(C2×C11) |
| Fitting, Hall | C3×C11×C169 ⋊ C22 |
| derived, Hall | C3×C169 ⋊ C22×C11 |
| Hall | C11×C169 ⋊ C2×D3 |
| Sylow | C169 ⋊ C2×D3×C11 |
| Hall | C3×C11 ⋊ C2×D169 |
| Sylow | C3 ⋊ C2×C11×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×D169 |
| commutator, cosocle, hypocenter | C3×C169 | C22×C11 |
| Frattini | C13 | D3×C11×D13 |
| Fitting | C3×C11×C169 | C22 |
| socle | C3×C11×C13 | C2×D13 |
| LCS | G ▷ C3×C169 | |
| UCS | C1 ◁ C11 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5577 |
2838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 25);