Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#63946 |
| Sylow | C33 ⋊ #137 |
328 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63946, #13171647, #13171653, … |
| maximal normal subgroup of | D3×#63946, #13171647, #13171653, … |
| maximal quotient of | C3×#10590447, C3×#10590463, C3×#10590487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3238);