Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D9×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C9⋊C8 |
| derived | C7×C9 ⋊ C3×C8 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C8 |
| Sylow | C7 ⋊ C3×C9⋊C8 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 48);