Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | #104×C11⋊C5 |
| unambiguous semidirect product | (C11×#104)⋊C5 |
| Fitting, Hall | C11×#104 ⋊ C5 |
| Sylow | C11 ⋊ C5×#104 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#453, #104×AGL(1,𝔽11), #72222331, … |
| maximal normal subgroup of | C11⋊C5×#453, #104×AGL(1,𝔽11), #72222331, … |
| maximal quotient of | C2×#104×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 57);