Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic11⋊C5 |
| unambiguous semidirect product | (C2×C11⋊C5)⋊C42 |
| unambiguous semidirect product | (C2×C4×Dic11)⋊C5 |
| derived, Sylow | C11 ⋊ C2×C42×C5 |
| Hall | C2×C4×Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C42 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C42×AGL(1,𝔽11), C2×#66993⋊C5, C2×#66901⋊C5, … |
| maximal normal subgroup of | C2×C42×AGL(1,𝔽11), C2×#66993⋊C5, C2×#66901⋊C5, … |
| maximal quotient of | C4×#4318⋊C5, M16×Dic11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 332);