Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×D21 |
| Fitting | C32×C7×Q8 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×Q8 |
| Sylow | C32 ⋊ Q8×D7 |
| Sylow | C7 ⋊ C3×D3×Q8 |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 852);