Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C4×D3×Dic3 |
| unambiguous semidirect product | (C3×D3)⋊(C3×C42) |
| derived | C32 ⋊ C2×C3×C42 |
| Sylow | C33 ⋊ C2×C42 |
562 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3×C3⋊C8, D3×#63554, Dic3×#3711, … |
| maximal normal subgroup of | D3×Dic3×C3⋊C8, D3×#63554, Dic3×#3711, … |
| maximal quotient of | C3×C4×D3×C3⋊C8, C3×D3×#803, C3×#10590318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3167);