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×PSU(3,𝔽2)⋊C4 |
| Sylow | C33 ⋊ #103 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×PSU(3,𝔽2)⋊C4, #89092⋊C4, #13180140, … |
| maximal normal subgroup of | D3×PSU(3,𝔽2)⋊C4, #89092⋊C4, #13180140, … |
| maximal quotient of | C3×PSU(3,𝔽2)⋊C8, C3×#10593157, C3×#10593158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4063);