Finite Group Databasebeta

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#72271494

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

3444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 35 points:

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

Polycyclic presentation:

2^9,3|a^2=g,d^2=g,e^2=h,h^2=i,b^a=bf,c^a=cg,c^b=cfi,d^b=dh,e^b=ehi,e^d=ei,f^a=fi,g^b=gi,h^b=hi,j^c=j^2

Conjugacy classes & character table

138 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, 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.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 10, 3, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);