Finite Group Databasebeta

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#72321073

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

Aliases

No aliases for this group.

Subgroups

3176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,b^2=ehij,c^2=ij,d^2=f,e^2=ij,h^2=i,i^2=j,b^a=bh,c^a=cf,c^b=cfi,d^a=dg,d^b=dg,d^c=defhj,e^b=ei,g^c=gj,h^a=hj,h^b=hi,i^b=ij

Conjugacy classes & character table

94 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, 1, F.5);;
gap> SetPower(coll, 2, F.5*F.8*F.9*F.10);;
gap> SetPower(coll, 3, F.9*F.10);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.6*F.8*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);