Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D176⋊C5 |
| Fitting | C11×C16 ⋊ C2×C5 |
| Hall | D176 ⋊ C5 |
| Hall | C11⋊C5 ⋊ D16 |
| Sylow | C11 ⋊ C5×D16 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^2,5,2^3,11|b^2=de,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^10,g^c=g^571 conjugacy classes — view the full character table.
| maximal subgroup of | #72248757, D16×AGL(1,𝔽11), #72248764 |
| maximal normal subgroup of | #72248757, D16×AGL(1,𝔽11), #72248764 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 10);