Finite Group DatabasebetaFinite Group Databasebeta| order | 756 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C7×C9 |
| unambiguous semidirect product | C3⋊(C22×C7×C9) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C7×C9) |
| Fitting | C2×C3×C7×C9 ⋊ C2 |
| derived | C3 ⋊ C22×C7×C9 |
| Hall | C3×C7×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C22×C7 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(756, 122);