Finite Group DatabasebetaFinite Group Databasebeta| order | 22022 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×D77 |
| unambiguous semidirect product | C7⋊(C11×C13×D11) |
| unambiguous semidirect product | C11⋊(C11×C13×D7) |
| Fitting, socle, Hall | C7×C112×C13 ⋊ C2 |
| derived | C7×C11 ⋊ C2×C11×C13 |
| Hall | C112×C13 ⋊ D7 |
| Hall | C7×C112 ⋊ C2×C13 |
| Sylow | C112 ⋊ C13×D7 |
| Hall | C7×C13 ⋊ C11×D11 |
| Sylow | C7 ⋊ C11×C13×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | D77 |
| commutator, cosocle, hypocenter | C7×C11 | C2×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112×C13 | C2 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C11×C13 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2002 |
5720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22022, 17);