Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C3×ΓL(1,𝔽8)⋊Q8 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C3×Q8) |
| unambiguous semidirect product | (C2×Dic14)⋊C32 |
| unambiguous semidirect product | (C2×C3×Dic14)⋊C3 |
| Hall | C2×Dic14 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×Q8 |
| Sylow | C7 ⋊ C2×C32×Q8 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 637);