Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #66972⋊C5 |
| Fitting | C11×Q16 ⋊ C2×C5 |
| Hall | #66972 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #135 |
| Sylow | C11 ⋊ C5×#135 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^3,5,2^2,11|b^2=f,c^2=f,e^2=f,b^a=bf,c^a=cf,g^a=g^10,c^b=ce,e^b=ef,e^c=ef,g^d=g^977 conjugacy classes — view the full character table.
| maximal subgroup of | #135×AGL(1,𝔽11), #72248764, #72254640, … |
| maximal normal subgroup of | #135×AGL(1,𝔽11), #72248764, #72254640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 329);