Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×D3×Dic12 |
| Sylow | C33 ⋊ C2×Q16 |
306 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63547, D3×#63549, D3×#63550, … |
| maximal normal subgroup of | D3×#63547, D3×#63549, D3×#63550, … |
| maximal quotient of | C3×D3×#818, C3×#10590682, C3×#10590684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3091);