Finite Group DatabasebetaFinite Group Databasebeta| order | 7040 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | #13070515 ⋊ C5 |
| Hall | C11⋊C5 ⋊ AGL(1,ℤ/16) |
| Sylow | C11 ⋊ C5×AGL(1,ℤ/16) |
308 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 95 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:
2^3,5,2^4,11|a^2=f,b^2=e,c^2=e,f^2=g,g^2=h,b^a=bfgh,c^a=cgh,e^a=eh,f^b=fg,f^c=fh,g^b=gh,i^b=i^10,i^c=i^10,i^d=i^9131 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×AGL(1,ℤ/16) |
| maximal normal subgroup of | AGL(1,𝔽11)×AGL(1,ℤ/16) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i");;
gap> coll := SingleCollector(F, [2, 2, 2, 5, 2, 2, 2, 2, 11]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 6, F.7);;
gap> SetPower(coll, 7, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.7*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.7);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.8);;
gap> SetConjugate(coll, 9, 2, F.9^10);;
gap> SetConjugate(coll, 9, 3, F.9^10);;
gap> SetConjugate(coll, 9, 4, F.9^9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);