Finite Group Databasebeta

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#72271532

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

Polycyclic presentation:

2^9,3|a^2=e,b^2=i,d^2=gi,e^2=h,h^2=i,b^a=beg,c^a=cf,c^b=cfg,d^a=dhi,d^b=dhi,e^b=eh,e^d=ei,f^b=fi,g^a=gi,g^b=gi,h^b=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.5);;
gap> SetPower(coll, 2, F.9);;
gap> SetPower(coll, 4, F.7*F.9);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 8, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.5*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*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);