Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×Dic57 |
| unambiguous semidirect product | C3⋊(Dic19×C121) |
| unambiguous semidirect product | C19⋊(Dic3×C121) |
| derived, Hall | C3×C19 ⋊ C4×C121 |
| Hall | C3×C19×C121 ⋊ C4 |
| Hall | C19×C121 ⋊ Dic3 |
| Hall | C3×C121 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic3×C121 |
| Sylow | C3 ⋊ Dic19×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C121 | D57 |
| commutator, hypocenter | C3×C19 | C4×C121 |
| Frattini | C2×C11 | C11×D57 |
| Fitting | C2×C3×C19×C121 | C2 |
| socle, prime radical, cosocle | C2×C3×C11×C19 | C2×C11 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C121 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27588 |
7260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 10);