Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C9×Dic3 |
| unambiguous semidirect product | (C2×C3)⋊(C4×C7×C9) |
| derived | C3 ⋊ C2×C4×C7×C9 |
| Hall | C3×C7×C9 ⋊ C2×C4 |
| Sylow | C3×C9 ⋊ C2×C4×C7 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D3×C7×C9, C4×C7×C9×Dic3 |
| maximal normal subgroup of | C2×C4×D3×C7×C9, C4×C7×C9×Dic3 |
| maximal quotient of | C2×C7×C9×C3⋊C8, C4×C7×C9×Dic3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 367);