Finite Group Databasebeta

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#72271517

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9,3|a^2=g,b^2=efi,d^2=g,e^2=h,f^2=i,h^2=i,b^a=be,c^a=cg,c^b=cfh,d^b=defhi,e^a=eh,e^d=eh,f^d=fi,g^b=gi,h^a=hi,h^d=hi,j^c=j^2

Conjugacy classes & character table

90 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, 3]);;
gap> SetPower(coll, 1, F.7);;
gap> SetPower(coll, 2, F.5*F.6*F.9);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 8, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.6*F.8*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 10, 3, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);