Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D112×C19⋊C3 |
| unambiguous semidirect product | (C11×D11)⋊(C2×C19⋊C3) |
| unambiguous semidirect product | (C19×D112)⋊C3 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C22×C3 |
| Hall | C19×D112 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C3×D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C22×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 81);