Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×#828 |
| Fitting | C33×Q16 ⋊ C2 |
| Sylow | C33 ⋊ SD32 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#828, C3×#10591038, C3×#10591039, … |
| maximal normal subgroup of | C3×D3×#828, C3×#10591038, C3×#10591039, … |
| maximal quotient of | C32×#4490, C32×#4491, C32×#4564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2083);