Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of C11⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C11⋊AGL(1,𝔽5) |
| Fitting | C2×C4×C5×C11 ⋊ C4 |
| derived, Hall | C5×C11 ⋊ C2×C42 |
| Sylow | C11 ⋊ C2×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4×Dic11 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1156);