Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×D3×(C2×D3)⋊C4 |
| Fitting | C2×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
666 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #13167995, #13167996, #13168000, … |
| maximal normal subgroup of | #13167995, #13167996, #13168000, … |
| maximal quotient of | C3×D3×#805, C3×#10590392, C3×D3×#806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3212);