Finite Group DatabasebetaFinite Group Databasebeta| order | 22066 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C59 · Schur multiplier (H2) = C1 |
| direct product | C17×D11×C59 |
| unambiguous semidirect product | C11⋊(C2×C17×C59) |
| Fitting, socle, Hall | C11×C17×C59 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C17×C59 |
| Hall | C11×C59 ⋊ C2×C17 |
| Hall | C11×C17 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C59 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C17×C59 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C59 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C17×C59 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11033 |
7021 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22066, 5);