Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#10624391⋊C2 |
| unambiguous semidirect product | #10624391⋊(C2×C19) |
| unambiguous semidirect product | ((C11⋊D11)⋊C3)⋊(C2×C19) |
| Fitting, socle, Hall | C112×C19 ⋊ C2×D3 |
| derived, Hall | C112⋊C3 ⋊ C22×C19 |
| Hall | C19×C112⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ C2×D3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #10624391⋊C2 |
| commutator, cosocle, hypocenter | C112⋊C3 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C112×C19 | C2×D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C19 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
589 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 75);