Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C4×C9×ΓL(1,𝔽8) |
| Fitting | C2×C4×C7×C9 ⋊ C3 |
| derived, Sylow | C7 ⋊ C2×C3×C4×C9 |
| Hall | C2×C4×C7 ⋊ C3×C9 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 310);