Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66943⋊C5 |
| Hall | #66943 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #125 |
| Sylow | C11 ⋊ C5×#125 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^3,5,2^2,11|a^2=f,b^2=e,c^2=f,c^a=cef,g^a=g^10,c^b=ce,g^d=g^980 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 301);