Finite Group Databasebeta

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#72226167

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3)(20,21,28,33,23,29,31,26,24,27,35,34,30,32,22,25);(5,10)(9,17)(11,18)(12,16)(21,27)(25,26)(29,32)(33,34);(5,9)(6,13)(7,14)(10,17)(11,12)(15,19)(16,18)(21,26)(22,28)(23,30)(25,27)(29,33)(31,35)(32,34);(2,3)(4,5)(6,9)(7,16)(8,10)(11,13)(12,14)(15,17)(18,19)(21,25)(22,28)(23,30)(26,27)(29,34)(31,35)(32,33)

Polycyclic presentation:

2^10,3|d^2=fh,e^2=gi,f^2=hj,g^2=i,h^2=j,b^a=be,c^a=ci,d^a=df,d^b=dfj,d^c=dj,e^a=eg,e^b=eg,f^a=fh,f^b=fh,g^a=gi,g^b=gi,h^a=hj,h^b=hj,k^a=k^2

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

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