Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C3⋊D3×Dic12 |
| Sylow | C33 ⋊ C2×Q16 |
432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 432 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) = 288 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #13154737, #13154738, #13154749, … |
| maximal normal subgroup of | #13154737, #13154738, #13154749, … |
| maximal quotient of | C3⋊D3×#818, #13159538, #13159540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3295);