Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C4×D3×C7⋊C9 |
| unambiguous semidirect product | (C4×D3×C7)⋊C9 |
| derived | C3×C7 ⋊ C2×C4×C9 |
| Hall | C3×C7⋊C9 ⋊ C2×C4 |
| Sylow | C7 ⋊ C4×D3×C9 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 187);