Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of AΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×AGL(1,𝔽8)⋊C9 |
| unambiguous semidirect product | (C3×AGL(1,𝔽8))⋊C9 |
| derived, Hall | AGL(1,𝔽8) ⋊ C3×C9 |
| Sylow | C23 ⋊ C3×C7⋊C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 441);