Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×AGL(1,𝔽9)⋊C4 |
| unambiguous semidirect product | AGL(1,𝔽9)⋊(C3×C4) |
| Sylow | C33 ⋊ #106 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4064);