Finite Group Databasebeta

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#72242339

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2099 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^10,5^2|a^2=d,b^2=e,c^2=f,d^2=h,e^2=g,h^2=i,i^2=j,b^a=bhij,d^b=di,e^a=ei,e^d=ej,g^a=gj,h^b=hj,k^a=k^2,k^c=k^3,k^d=k^4,k^f=k^4,l^a=kl,l^c=l^3,l^d=k^3l,l^f=l^4

Conjugacy classes & character table

316 conjugacy classes — view the full character table.

Relationships

GAP

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", "j", "k", "l");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5]);;
gap> SetPower(coll, 1, F.4);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.8);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 11, 1, F.11^2);;
gap> SetConjugate(coll, 11, 3, F.11^3);;
gap> SetConjugate(coll, 11, 4, F.11^4);;
gap> SetConjugate(coll, 11, 6, F.11^4);;
gap> SetConjugate(coll, 12, 1, F.11*F.12);;
gap> SetConjugate(coll, 12, 3, F.12^3);;
gap> SetConjugate(coll, 12, 4, F.11^3*F.12);;
gap> SetConjugate(coll, 12, 6, F.12^4);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);