Finite Group Databasebeta

?

← Prev (#72271715) Next (#72271717) →

#72271716

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9,3|a^2=g,b^2=e,c^2=g,d^2=g,e^2=h,h^2=i,b^a=bf,c^a=cg,c^b=cfghi,d^b=defgh,e^a=ei,e^c=ei,e^d=eh,f^a=fi,f^b=fi,g^b=gi,h^d=hi,j^d=j^2

Conjugacy classes & character table

93 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);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 8, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7*F.8*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.6*F.7*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 10, 4, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);