Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of C49⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C49⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊Dic49 |
| unambiguous semidirect product | (C2×C49)⋊AGL(1,𝔽5) |
| Fitting | C2×C5×C49 ⋊ C4 |
| derived, Hall | C5×C49 ⋊ C2×C4 |
| Sylow | C49 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×Dic49 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 490 |
202 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 35);