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×#827 |
| Sylow | C33 ⋊ SD32 |
244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#827, C3×#10591028, C3×#10591029, … |
| maximal normal subgroup of | C3×D3×#827, C3×#10591028, C3×#10591029, … |
| maximal quotient of | C32×#4490, C32×#4492, C32×#4562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2082);