Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#63747 |
| Sylow | C33 ⋊ #95 |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593164, #13165117, D3×#63747, … |
| maximal normal subgroup of | C3×#10593164, #13165117, D3×#63747, … |
| maximal quotient of | C3×#10590090, C3×#10590091, C3×#10590092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2768);