Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C3⋊#168 |
| unambiguous semidirect product | (C2×C3)⋊(C7×#168) |
| derived, Hall | C3×C5 ⋊ C2×C7×C8 |
| Hall | C3×C5×C7 ⋊ C2×C8 |
| Hall | C5×C7 ⋊ C2×C3⋊C8 |
| Hall | C3×C7 ⋊ C2×#168 |
| Sylow | C5 ⋊ C2×C7×C3⋊C8 |
| Sylow | C3 ⋊ C2×C7×#168 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1680 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 362);