Finite Group DatabasebetaFinite Group Databasebeta| order | 840 |
| isoclinism | isoclinic class of D5×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic5×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C2×C7×Dic5)⋊C3 |
| derived, Hall | C5×C7 ⋊ C2×C3×C4 |
| Hall | C2×C7×Dic5 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×C4 |
| Sylow | C7 ⋊ C2×C3×Dic5 |
| Sylow | C5 ⋊ C2×C4×ΓL(1,𝔽8) |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(840, 31);