Finite Group Databasebeta

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#72226131

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10,3|b^2=e,c^2=f,d^2=gi,f^2=h,g^2=ij,i^2=j,b^a=bf,c^a=cfh,c^b=ch,d^a=dg,d^b=dij,e^a=eh,e^d=ej,f^a=fh,g^a=gi,g^b=gj,i^a=ij,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, 2, F.5);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7*F.9);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 11, 1, F.11^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);