Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#41×ΓL(1,𝔽8) |
| Fitting, Hall | C5×C7×#41 ⋊ C3 |
| Hall | C7×#41 ⋊ C3×C5 |
| Hall | C5×C7 ⋊ C3×#41 |
| Sylow | C7 ⋊ C3×C5×#41 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#41×ΓL(1,𝔽8), C5×ΓL(1,𝔽8)×AGL(1,ℤ/8), ΓL(1,𝔽8)×#4095, … |
| maximal normal subgroup of | D5×#41×ΓL(1,𝔽8), C5×ΓL(1,𝔽8)×AGL(1,ℤ/8), ΓL(1,𝔽8)×#4095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 843);