Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C11 |
| direct product | C19×#13089721 |
| Fitting, socle, Hall | C112×C19 ⋊ Dic3 |
| derived, Hall | C112⋊C3 ⋊ C4×C19 |
| Hall | C19×C112⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ Dic3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #13089721 |
| commutator, hypocenter | C112⋊C3 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C112×C19 | Dic3 |
| prime radical | C19×(C11⋊D11)⋊C3 | C2 |
| cosocle | (C11⋊D11)⋊C3 | C2×C19 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1254 |
304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 69);