Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5×C7 · Schur multiplier (H2) = C4 |
| direct product | C4×C5×C7×Dic3 |
| unambiguous semidirect product | C3⋊(C42×C5×C7) |
| derived, Sylow | C3 ⋊ C42×C5×C7 |
| Hall | C3×C5×C7 ⋊ C42 |
| Hall | C3×C7 ⋊ C42×C5 |
| Hall | C3×C5 ⋊ C42×C7 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1680 |
840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 332);