Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | D12×C3⋊Dic3 |
| Sylow | C33 ⋊ C4×D4 |
668 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 668 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) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #13154765, #13154767, #13155608, … |
| maximal normal subgroup of | #13154765, #13154767, #13155608, … |
| maximal quotient of | D12×C3⋊(C3⋊C8), #13158922, #13158944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3457);