Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#226 |
199 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64196, D3×#64198, #13180255, … |
| maximal normal subgroup of | D3×#64196, D3×#64198, #13180255, … |
| maximal quotient of | C3×Dic3×#226, C3×#10593193, C3×#10593201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4132);