Finite Group Databasebeta

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#72219802

• supersolvable
• metabelian
• solvable
• monomial
• stem
• rational
• ambivalent

Aliases

No aliases for this group.

Splittings

Subgroups

At least 8054 conjugacy classes of subgroups; only the 926 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^10,3^2|a^2=j,b^2=f,f^2=h,g^2=i,i^2=j,b^a=bg,c^b=cf,d^b=dh,f^a=fi,f^c=fh,g^a=gij,g^c=gij,g^d=gj,h^a=hj,i^a=ij,i^c=ij,k^a=k^2,k^e=k^2,l^a=k^2l,l^e=l^2

Conjugacy classes & character table

216 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, 3, 3]);;
gap> SetPower(coll, 1, F.10);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> SetConjugate(coll, 11, 1, F.11^2);;
gap> SetConjugate(coll, 11, 5, F.11^2);;
gap> SetConjugate(coll, 12, 1, F.11^2*F.12);;
gap> SetConjugate(coll, 12, 5, F.12^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);