Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #66995⋊C5 |
| Fitting | C2×Q8×C11 ⋊ C2×C5 |
| Hall | #66995 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #137 |
| Sylow | C11 ⋊ C5×#137 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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=f,e^2=f,c^a=ce,e^a=ef,g^a=g^10,c^b=cf,e^c=ef,g^d=g^965 conjugacy classes — view the full character table.
| maximal subgroup of | #72254622, #137×AGL(1,𝔽11), #72254640, … |
| maximal normal subgroup of | #72254622, #137×AGL(1,𝔽11), #72254640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 354);