Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×C4×D3×A4 |
| unambiguous semidirect product | (C22×C4×D3)⋊C32 |
| unambiguous semidirect product | (C22×C3×C4×D3)⋊C3 |
| Fitting | C22×C32×C4 ⋊ C2×C3 |
| derived | C22×C3 ⋊ C2×C32×C4 |
383 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4442);