Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×C7×C8 |
| Fitting | C32×C7×C8 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C7×C8 |
| Hall | C32×C7 ⋊ C2×C8 |
| Sylow | C32 ⋊ C2×C7×C8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×C8×C9, C2×C3×D3×C7×C8 |
| maximal normal subgroup of | D3×C7×C8×C9, C2×C3×D3×C7×C8 |
| maximal quotient of | D3×C7×C8×C9, C2×C3×D3×C7×C8, C3×C7×C8×Dic3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 426);