Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63626 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×#63627 |
| Fitting | C33×C16 ⋊ C2 |
| Sylow | C33 ⋊ SD32 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#800, C3×#10590232, C3×#10590238, … |
| maximal normal subgroup of | C3×D3×#800, C3×#10590232, C3×#10590238, … |
| maximal quotient of | C3×#10589371, C3×#10589375, C3×#10589369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2096);