Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×C3×C4)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C3×C4×C7)⋊A4 |
| Fitting | C22×C3×C4×C7 ⋊ C3 |
| derived | C22×C7 ⋊ C32×C4 |
| Hall | C22×C4×C7 ⋊ C32 |
| Sylow | C22×C4 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C4×A4 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 823);