Finite Group Databasebeta

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#72270262

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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=cfhi,d^b=dh,e^a=eh,e^d=ei,g^b=gi,h^a=hi,j^c=j^2

Conjugacy classes & character table

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