Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6290 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×(C2×D3)⋊(C3⋊Dic3) |
| Sylow | C33 ⋊ C2×C22⋊C4 |
1008 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #13154843, Dic3×(C2×D3)⋊Dic3, #13156695, … |
| maximal normal subgroup of | #13154843, Dic3×(C2×D3)⋊Dic3, #13156695, … |
| maximal quotient of | #13160254, #13160266, C2×(C2×D3)⋊(C3⋊(C3⋊C8)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3568);