Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#64196 |
183 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 96 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64196, #13180235, #13180245, … |
| maximal normal subgroup of | D3×#64196, #13180235, #13180245, … |
| maximal quotient of | C3×#10593194, C3×#10593195, C3×#10593197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4128);