Finite Group DatabasebetaFinite Group Databasebeta| order | 27566 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C179 · Schur multiplier (H2) = C1 |
| direct product | C7×D11×C179 |
| unambiguous semidirect product | C11⋊(C2×C7×C179) |
| Fitting, socle, Hall | C7×C11×C179 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C7×C179 |
| Hall | C11×C179 ⋊ C2×C7 |
| Hall | C7×C11 ⋊ C2×C179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C179 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C7×C179 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C179 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C7×C179 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13783 |
8771 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27566, 3);