Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C8×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C2×C7×C8)⋊C32 |
| unambiguous semidirect product | (C2×C3×C7×C8)⋊C3 |
| Fitting | C2×C3×C7×C8 ⋊ C3 |
| derived, Sylow | C7 ⋊ C2×C32×C8 |
| Hall | C2×C7×C8 ⋊ C32 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 403);