Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | #67×C3⋊Dic3 |
| Sylow | C33 ⋊ C4×D4 |
700 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #67×#622, #13166618, #67⋊#622, … |
| maximal normal subgroup of | #67×#622, #13166618, #67⋊#622, … |
| maximal quotient of | C3⋊Dic3×Dic3⋊C4, #13160451, #13160519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3586);