Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #66950⋊C5 |
| Fitting | C11×C4⋊C4 ⋊ C2×C5 |
| Hall | #66950 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C22⋊Q8 |
| Sylow | C11 ⋊ C5×C22⋊Q8 |
148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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=ef,c^a=ce,g^a=g^10,c^b=cf,g^d=g^980 conjugacy classes — view the full character table.
| maximal subgroup of | #72248832, C22⋊Q8×AGL(1,𝔽11), #72248843, … |
| maximal normal subgroup of | #72248832, C22⋊Q8×AGL(1,𝔽11), #72248843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 307);