Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×AGL(1,𝔽9) |
| Fitting | C2×C32×C9 ⋊ C8 |
| derived | C32 ⋊ C2×C8×C9 |
| Sylow | C32×C9 ⋊ C2×C8 |
89 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2965);