Finite Group DatabasebetaFinite Group Databasebeta| order | 24222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D11×C367⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C367⋊C3) |
| unambiguous semidirect product | (D11×C367)⋊C3 |
| Fitting, socle, derived, Hall | C11×C367 ⋊ C2×C3 |
| Hall | C11×C367⋊C3 ⋊ C2 |
| Hall | D11×C367 ⋊ C3 |
| Sylow | C367 ⋊ C3×D11 |
| Sylow | C11 ⋊ C2×C367⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C367 | C2×C3 |
| LCS | G ▷ C11×C367 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4037 |
875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24222, 11);