Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×C4⋊(C3⋊C8) |
| unambiguous semidirect product | C4⋊(C9×C3⋊C8) |
| Sylow | C3×C9 ⋊ C4⋊C8 |
144 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13134934, #13134935, #13134936, … |
| maximal normal subgroup of | #13134934, #13134935, #13134936, … |
| maximal quotient of | C9×#4457, C9×#4458, C9×C4⋊(C3⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 333);