Finite Group DatabasebetaFinite Group Databasebeta| order | 22428 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×Dic89 |
| unambiguous semidirect product | (C7×Dic89)⋊C32 |
| unambiguous semidirect product | (C3×C7×Dic89)⋊C3 |
| derived, Hall | C7×C89 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C89 ⋊ C4 |
| Hall | C7×Dic89 ⋊ C32 |
| Sylow | C89 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C32×Dic89 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7476 |
1380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22428, 44);