Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×(C3⋊D9)⋊C4 |
| unambiguous semidirect product | (C3⋊D9)⋊C42 |
| derived, Sylow | C3×C9 ⋊ C2×C42 |
378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C8×(C3⋊D9)⋊C4, #13138161, #13138162, … |
| maximal normal subgroup of | C8×(C3⋊D9)⋊C4, #13138161, #13138162, … |
| maximal quotient of | C4×(C3⋊D9)⋊C8, #13137150, #13137151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 946);