Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| direct product | C2×(C11⋊D11)⋊(C19⋊C3) |
| unambiguous semidirect product | (C2×C11⋊D11)⋊(C19⋊C3) |
| Fitting, socle | C2×C112×C19 ⋊ C2×C3 |
| derived, Hall | C112×C19 ⋊ C22×C3 |
| Hall | C2×C19×C11⋊D11 ⋊ C3 |
| Hall | C19⋊(C112⋊C3) ⋊ C22 |
| Hall | C2×C11⋊D11 ⋊ C19⋊C3 |
| Sylow | C112 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C2×(C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C11⋊D11)⋊(C19⋊C3) |
| commutator, cosocle, hypocenter | C112×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C19 | C2×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1254 |
796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 89);