Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D16×C11⋊C5 |
| unambiguous semidirect product | (C11×D16)⋊C5 |
| Fitting, Hall | C11×D16 ⋊ C5 |
| Sylow | C11 ⋊ C5×D16 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#509, D16×AGL(1,𝔽11), #72248762 |
| maximal normal subgroup of | C11⋊C5×#509, D16×AGL(1,𝔽11), #72248762 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 64);