Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | C19⋊C3×C11⋊Dic11 |
| unambiguous semidirect product | C11⋊(Dic11×C19⋊C3) |
| derived, Hall | C112×C19 ⋊ C3×C4 |
| Hall | C19×C11⋊Dic11 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊C3×C11⋊D11 |
| commutator, hypocenter | C112×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C112×C19 | C2×C3 |
| prime radical | C2×C112×C19⋊C3 | C2 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9196 |
1116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 40);