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#72320707

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

Aliases

No aliases for this group.

Subgroups

4739 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Polycyclic presentation:

2^10|b^2=f,d^2=f,g^2=i,i^2=j,c^b=cg,d^a=dh,d^c=dij,e^a=ej,e^d=ej,f^c=fj,g^b=gi,g^c=gij,g^d=gj,i^b=ij,i^c=ij

Conjugacy classes & character table

118 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);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);