Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×(C7⋊C8)⋊C9 |
| unambiguous semidirect product | (C2×C7⋊C8)⋊C9 |
| unambiguous semidirect product | (C2×C7⋊C9)⋊C8 |
| derived, Sylow | C7 ⋊ C2×C8×C9 |
| Hall | C2×C7⋊C8 ⋊ C9 |
| Hall | C7⋊C9 ⋊ C2×C8 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 12);