Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic627 |
| unambiguous semidirect product | C3⋊(C11×Dic209) |
| unambiguous semidirect product | C11⋊(C11×Dic57) |
| unambiguous semidirect product | C19⋊(C11×Dic33) |
| derived | C3×C11×C19 ⋊ C4×C11 |
| Hall | C3×C112×C19 ⋊ C4 |
| Hall | C112×C19 ⋊ Dic3 |
| Hall | C3×C112 ⋊ Dic19 |
| Sylow | C112 ⋊ Dic57 |
| Hall | C3×C19 ⋊ C11×Dic11 |
| Sylow | C19 ⋊ C11×Dic33 |
| Sylow | C3 ⋊ C11×Dic209 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D627 |
| commutator, hypocenter | C3×C11×C19 | C4×C11 |
| Frattini | C2 | C11×D627 |
| Fitting, socle, prime radical | C2×C3×C112×C19 | C2 |
| cosocle | C2×C3×C11×C19 | C2×C11 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C2×C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2508 |
6930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 54);