Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×C9⋊C8 |
| derived, Sylow | C3×C9 ⋊ C22×C8 |
250 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×C9⋊C8, D3×#63362, #13137208, … |
| maximal normal subgroup of | C4×D3×C9⋊C8, D3×#63362, #13137208, … |
| maximal quotient of | Dic6×C9⋊C8, #13137020, #13137114, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 842);