Finite Group Databasebeta

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#72214124

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Subgroups

1805 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^10|a^2=j,b^2=gij,c^2=e,d^2=efg,e^2=hij,f^2=hj,g^2=i,h^2=j,i^2=j,b^a=bg,c^a=cgij,c^b=cf,d^a=di,d^b=dhij,d^c=dhij,e^a=ei,e^b=eh,f^a=fj,f^b=fhj,f^c=fj,f^d=fj,g^a=gij,g^c=gj,g^d=gj,h^b=hj,i^a=ij

Conjugacy classes & character table

88 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.10);;
gap> SetPower(coll, 2, F.7*F.9*F.10);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.5*F.6*F.7);;
gap> SetPower(coll, 5, F.8*F.9*F.10);;
gap> SetPower(coll, 6, F.8*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);