Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #66997⋊C5 |
| Hall | #66997 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C4⋊Q8 |
| Sylow | C11 ⋊ C5×C4⋊Q8 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^3,5,2^2,11|a^2=f,b^2=f,c^2=f,b^a=bf,c^a=ce,g^a=g^10,c^b=cf,g^d=g^980 conjugacy classes — view the full character table.
| maximal subgroup of | #72248880, C4⋊Q8×AGL(1,𝔽11), #72248924, … |
| maximal normal subgroup of | #72248880, C4⋊Q8×AGL(1,𝔽11), #72248924, … |
| maximal quotient of | #72249021 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 351);