Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D3×Dic14 |
| unambiguous semidirect product | (D3×C7)⋊(C5×Q8) |
| Hall | C3×C5×C7 ⋊ C2×Q8 |
| Hall | C5×C7 ⋊ D3×Q8 |
| Hall | C3×C7 ⋊ C2×C5×Q8 |
| Hall | C3×C5 ⋊ C2×Dic14 |
| Sylow | C7 ⋊ C5×D3×Q8 |
| Sylow | C3 ⋊ C2×C5×Dic14 |
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 840 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 681);