Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic2299 |
| unambiguous semidirect product | C121⋊(C3×Dic19) |
| derived, Hall | C19×C121 ⋊ C3×C4 |
| Hall | C3×C19×C121 ⋊ C4 |
| Hall | C3×C121 ⋊ Dic19 |
| Sylow | C121 ⋊ C3×Dic19 |
| Hall | C3×C19 ⋊ Dic121 |
| Sylow | C19 ⋊ C3×Dic121 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27588 |
6906 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 8);