Finite Group DatabasebetaFinite Group Databasebeta| order | 22066 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D649 |
| unambiguous semidirect product | C11⋊(C17×D59) |
| unambiguous semidirect product | C59⋊(C17×D11) |
| Fitting, socle, Hall | C11×C17×C59 ⋊ C2 |
| derived, Hall | C11×C59 ⋊ C2×C17 |
| Hall | C17×C59 ⋊ D11 |
| Hall | C11×C17 ⋊ D59 |
| Sylow | C59 ⋊ C17×D11 |
| Sylow | C11 ⋊ C17×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D649 |
| commutator, cosocle, hypocenter | C11×C59 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C59 | C2 |
| LCS | G ▷ C11×C59 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11033 |
5542 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22066, 6);