Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×(C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic3×(C22⋊C9)⋊C2 |
| unambiguous semidirect product | (C3×(C22⋊C9)⋊C2)⋊C4 |
| derived | C3×C22⋊C9 ⋊ C2×C4 |
211 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×(C22⋊C9)⋊C2, #13164155, #13164162, … |
| maximal normal subgroup of | Dic6×(C22⋊C9)⋊C2, #13164155, #13164162, … |
| maximal quotient of | C3⋊C8×(C22⋊C9)⋊C2, #13146266, Dic3×#3688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2229);