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×Dic3×D9 |
| unambiguous semidirect product | (C3×D9)⋊C42 |
| derived, Sylow | C3×C9 ⋊ C2×C42 |
354 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 127 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 | C8×Dic3×D9, D9×Dic3⋊C8, #13138158, … |
| maximal normal subgroup of | C8×Dic3×D9, D9×Dic3⋊C8, #13138158, … |
| maximal quotient of | C4×D9×C3⋊C8, D9×#803, #13137147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 939);