Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | D3×#3788 |
| Sylow | C33 ⋊ C2×M16 |
276 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63727, D3×#63728, #13165151, … |
| maximal normal subgroup of | D3×#63727, D3×#63728, #13165151, … |
| maximal quotient of | Dic3×#3788, #13166302, #13166305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4216);