Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C19×C121 ⋊ C22×C3 |
| Hall | D19×D121 ⋊ C3 |
| Hall | C19⋊C3×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D19⋊C3 |
| Hall | C19⋊C3 ⋊ C2×D121 |
| Sylow | C19 ⋊ C2×C3×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C19×C121 | C22×C3 |
| Frattini | C11 | D11×D19⋊C3 |
| socle | C11×C19 | C2×C3×D11 |
| LCS | G ▷ C19×C121 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2299 |
558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 14);