Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C112×C19 ⋊ C22×C3 |
| derived | C11×C19 ⋊ C22×C3×C11 |
| Hall | C11×D11×D19 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ C2×D19⋊C3 |
| Hall | C19⋊C3 ⋊ C2×C11×D11 |
| Sylow | C19 ⋊ C2×C3×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D11×D19⋊C3 |
| commutator, cosocle, hypocenter | C11×C19 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C19 | C22×C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C11 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
693 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 78);