Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic3×ΓL(1,𝔽8) |
| derived | C3×C7 ⋊ C22×C3×C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C22×C4 |
| Sylow | C7 ⋊ C22×C3×Dic3 |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 655);