Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | C19⋊C3×#92150 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C3×C4 |
| Hall | C19×#92150 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ C3×#92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C19 | C3×C4 |
| prime radical | C19⋊C3×C11⋊D11 | C2 |
| cosocle | C19×C11⋊D11 | C2×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 65);