Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×Q8×D15 |
| Fitting | C3×C5×C7×Q8 ⋊ C2 |
| Hall | C3×C5×C7 ⋊ C2×Q8 |
| Hall | C5×C7 ⋊ D3×Q8 |
| Hall | C3×C7 ⋊ Q8×D5 |
| Hall | C3×C5 ⋊ C2×C7×Q8 |
| Sylow | C5 ⋊ D3×C7×Q8 |
| Sylow | C3 ⋊ C7×Q8×D5 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 840 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 906);