Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D420 |
| Fitting | C2×C3×C4×C5×C7 ⋊ C2 |
| Hall | C3×C5×C7 ⋊ C2×D4 |
| Hall | C5×C7 ⋊ C2×D12 |
| Hall | C3×C7 ⋊ C2×D20 |
| Hall | C3×C5 ⋊ C2×D28 |
| Sylow | C7 ⋊ C2×D60 |
| Sylow | C5 ⋊ C2×D84 |
| Sylow | C3 ⋊ C2×D140 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 840 |
426 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 912);