Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of C3⋊(C7⋊AGL(1,𝔽5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×C3⋊(C7⋊AGL(1,𝔽5)) |
| Fitting | C3×C4×C5×C7 ⋊ C4 |
| derived, Hall | C3×C5×C7 ⋊ C42 |
| Hall | C5×C7 ⋊ C4×Dic3 |
| Hall | C3×C7 ⋊ C4×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ C4×Dic7 |
| Sylow | C7 ⋊ C4×ΓL(1,𝔽16) |
| Sylow | C5 ⋊ C4×Dic21 |
| Sylow | C3 ⋊ C4×C7⋊AGL(1,𝔽5) |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 420 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 646);