Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #66946⋊C5 |
| Fitting | C11×C4⋊C4 ⋊ C2×C5 |
| Hall | #66946 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C4×D4 |
| Sylow | C11 ⋊ C4×C5×D4 |
188 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^3,5,2^2,11|b^2=f,c^2=e,b^a=bf,g^a=g^10,c^b=cf,g^d=g^9110 conjugacy classes — view the full character table.
| maximal subgroup of | #72248709, C4×D4×AGL(1,𝔽11), #72248717, … |
| maximal normal subgroup of | #72248709, C4×D4×AGL(1,𝔽11), #72248717, … |
| maximal quotient of | #72248709, #72248737, #72276420 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 304);