Finite Group DatabasebetaFinite Group Databasebeta| order | 22242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3707 |
| unambiguous semidirect product | C11⋊(C3×D337) |
| Fitting, socle, Hall | C3×C11×C337 ⋊ C2 |
| derived, Hall | C11×C337 ⋊ C2×C3 |
| Hall | C3×C337 ⋊ D11 |
| Sylow | C337 ⋊ C3×D11 |
| Hall | C3×C11 ⋊ D337 |
| Sylow | C11 ⋊ C3×D337 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3707 |
| commutator, cosocle, hypocenter | C11×C337 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C337 | C2 |
| LCS | G ▷ C11×C337 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11121 |
5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22242, 5);