Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×ΓL(1,𝔽8)×Dic10 |
| unambiguous semidirect product | (C2×C5)⋊(Q8×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C2×C7×Dic10)⋊C3 |
| Hall | C2×C7×Dic10 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×Q8 |
| Hall | C5×C7 ⋊ C2×C3×Q8 |
| Sylow | C7 ⋊ C2×C3×Dic10 |
| Sylow | C5 ⋊ C2×Q8×ΓL(1,𝔽8) |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 585);