Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×Q16×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C7×Q16)⋊C32 |
| unambiguous semidirect product | (C3×C7×Q16)⋊C3 |
| Fitting | C3×C7×Q16 ⋊ C3 |
| Hall | C7×Q16 ⋊ C32 |
| Sylow | C7 ⋊ C32×Q16 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 407);