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#72257239

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

Aliases

No aliases for this group.

Subgroups

3687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,d^2=eh,e^2=ij,f^2=j,i^2=j,b^a=bh,c^a=cfij,d^a=de,d^b=dg,d^c=de,e^a=ei,e^c=ei,e^d=ej,f^c=fj,g^a=gj,h^d=hj,i^a=ij,i^c=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.6);;
gap> SetPower(coll, 4, F.5*F.8);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
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.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);