Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C121 · Schur multiplier (H2) = C2 |
| direct product | D3×D19×C121 |
| unambiguous semidirect product | (D3×C19)⋊(C2×C121) |
| unambiguous semidirect product | (C3×D19)⋊(C2×C121) |
| unambiguous semidirect product | D57⋊(C2×C121) |
| Fitting, Hall | C3×C19×C121 ⋊ C22 |
| derived, Hall | C3×C19 ⋊ C22×C121 |
| Hall | C19×C121 ⋊ C2×D3 |
| Hall | C3×C121 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D3×C121 |
| Sylow | C3 ⋊ C2×D19×C121 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6897 |
3993 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 19);