Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of AΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×AGL(1,𝔽8)⋊C9 |
| unambiguous semidirect product | AGL(1,𝔽8)⋊(C2×C9) |
| unambiguous semidirect product | (C2×AGL(1,𝔽8))⋊C9 |
| derived | AGL(1,𝔽8) ⋊ C2×C9 |
| Hall | C2×AGL(1,𝔽8) ⋊ C9 |
| Sylow | C24 ⋊ C7⋊C9 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 126 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 498);