Finite Group DatabasebetaFinite Group Databasebeta| order | 22044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C167 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C11×C167 |
| unambiguous semidirect product | C3⋊(C22×C11×C167) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C11×C167) |
| Fitting, socle | C2×C3×C11×C167 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C11×C167 |
| Hall | C3×C11×C167 ⋊ C22 |
| Hall | C3×C167 ⋊ C22×C11 |
| Hall | C3×C11 ⋊ C22×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C167 | D3 |
| commutator, cosocle, hypocenter | C3 | C22×C11×C167 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11×C167 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C11×C167 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11022 |
11022 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22044, 21);