Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C19⋊C3×D121 |
| unambiguous semidirect product | C121⋊(C22×C19⋊C3) |
| unambiguous semidirect product | (C2×C121)⋊(C2×C19⋊C3) |
| unambiguous semidirect product | (C2×C19×D121)⋊C3 |
| Fitting | C2×C19×C121 ⋊ C2×C3 |
| derived, Hall | C19×C121 ⋊ C22×C3 |
| Hall | C2×C19×D121 ⋊ C3 |
| Hall | C19⋊C3×C121 ⋊ C22 |
| Sylow | C121 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C2×C3×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊C3×D121 |
| commutator, cosocle, hypocenter | C19×C121 | C22×C3 |
| Frattini | C11 | C2×D11×C19⋊C3 |
| Fitting | C2×C19×C121 | C2×C3 |
| socle | C2×C11×C19 | C3×D11 |
| LCS | G ▷ C19×C121 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4598 |
1116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 17);