Finite Group Databasebeta

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#72257497

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Subgroups

3703 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2)(3,4)(12,26)(16,29)(18,34)(28,30);(1,3,4,2)(5,6,10,15,11,14,23,7)(8,12,27,16,20,26,21,29)(9,13,24,32,25,31,36,17)(18,22,30,33,34,19,28,35);(2,3)(5,7,10,14,11,15,23,6)(8,18,21,30,20,34,27,28)(9,13,24,17,25,31,36,32)(12,19,16,33,26,22,29,35);(5,8,9,22,23,27,36,33,11,20,25,19,10,21,24,35)(6,12,13,30,7,16,17,34,14,26,31,28,15,29,32,18)

Polycyclic presentation:

2^10|b^2=fi,c^2=gi,d^2=eh,e^2=ij,i^2=j,b^a=bf,c^a=cf,c^b=cfg,d^a=dg,d^b=dgj,d^c=de,e^c=ei,e^d=ej,f^d=fj,g^b=gj,g^c=gj,h^d=hj,i^c=ij

Conjugacy classes & character table

100 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, 2]);;
gap> SetPower(coll, 2, F.6*F.9);;
gap> SetPower(coll, 3, F.7*F.9);;
gap> SetPower(coll, 4, F.5*F.8);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
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.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);