Finite Group DatabasebetaFinite Group Databasebeta| order | 22022 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×D143 |
| unambiguous semidirect product | C11⋊(C7×C11×D13) |
| unambiguous semidirect product | C13⋊(C7×C11×D11) |
| Fitting, socle, Hall | C7×C112×C13 ⋊ C2 |
| derived | C11×C13 ⋊ C2×C7×C11 |
| Hall | C112×C13 ⋊ C2×C7 |
| Hall | C7×C112 ⋊ D13 |
| Sylow | C112 ⋊ C7×D13 |
| Hall | C7×C13 ⋊ C11×D11 |
| Sylow | C13 ⋊ C7×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | D143 |
| commutator, cosocle, hypocenter | C11×C13 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112×C13 | C2 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C7×C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2002 |
5621 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22022, 12);