Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)×#634 |
| Hall | C32×ΓL(1,𝔽8) ⋊ Q8 |
| Sylow | C7 ⋊ C3×#634 |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 648);