Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C4×C5×C7×A4 |
| unambiguous semidirect product | (C22×C4)⋊(C3×C5×C7) |
| unambiguous semidirect product | (C22×C4×C5)⋊(C3×C7) |
| Fitting, Hall | C22×C4×C5×C7 ⋊ C3 |
| derived | C22 ⋊ C3×C4×C5×C7 |
| Hall | C22×C4×C7 ⋊ C3×C5 |
| Hall | C22×C4×C5 ⋊ C3×C7 |
| Sylow | C22×C4 ⋊ C3×C5×C7 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 420 |
560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 844);