Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C7 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×C7×Dic3 |
| unambiguous semidirect product | C3⋊(C3×C42×C7) |
| derived | C3 ⋊ C3×C42×C7 |
| Hall | C32×C7 ⋊ C42 |
| Sylow | C32 ⋊ C42×C7 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C7×C9×Dic3, C3×C42×D3×C7, C3×C7×C8×Dic3 |
| maximal normal subgroup of | C4×C7×C9×Dic3, C3×C42×D3×C7, C3×C7×C8×Dic3 |
| maximal quotient of | C4×C7×C9×Dic3, C3×C4×C7×C3⋊C8, C3×C7×C8×Dic3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 433);