Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| direct product | D19×(C11⋊D11)⋊C3 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C22×C3 |
| Hall | D19×C11⋊D11 ⋊ C3 |
| Hall | C19×C112⋊C3 ⋊ C22 |
| Hall | C112⋊C3 ⋊ C2×D19 |
| Sylow | C112 ⋊ C2×C3×D19 |
| Sylow | C19 ⋊ C2×(C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C22×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
286 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 68);