Finite Group DatabasebetaFinite Group Databasebeta| order | 25668 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic23×C31⋊C3 |
| unambiguous semidirect product | C23⋊(C3×C4×C31⋊C3) |
| unambiguous semidirect product | (C31×Dic23)⋊C32 |
| unambiguous semidirect product | (C3×C31×Dic23)⋊C3 |
| derived, Hall | C23×C31 ⋊ C32×C4 |
| Hall | C3×C23×C31⋊C3 ⋊ C4 |
| Hall | C31×Dic23 ⋊ C32 |
| Sylow | C31 ⋊ C32×Dic23 |
| Sylow | C23 ⋊ C3×C4×C31⋊C3 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8556 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25668, 38);