Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)⋊#170 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊#170 |
| unambiguous semidirect product | (C2×C7⋊#170)⋊C3 |
| derived, Hall | C5×C7 ⋊ C2×C3×C8 |
| Hall | C2×C7⋊#170 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×C8 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#170 |
| Sylow | C7 ⋊ C2×C3×#170 |
| Sylow | C5 ⋊ C2×ΓL(1,𝔽8)⋊C8 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 428);