Finite Group Databasebeta

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#72308786

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

Aliases

No aliases for this group.

Subgroups

4471 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)(8,9)(10,12)(13,14)(15,20)(16,18)(17,19)(22,26)(23,30)(24,31)(28,34)(32,35)(33,36);(2,4)(6,9)(7,12);(13,15,17,16)(14,18,19,20)(21,22)(23,29)(24,32)(25,26)(27,30)(28,33)(31,34)(35,36);(5,7,8,12)(6,10,9,11)(13,16,17,15)(14,18,19,20)(21,23,25,30)(22,27,26,29)(24,31,33,36)(28,34,32,35);(6,9)(10,11)(14,19)(18,20)(21,24,23,31,25,33,30,36)(22,28,29,35,26,32,27,34)

Polycyclic presentation:

2^10|a^2=f,c^2=ghj,d^2=h,e^2=i,i^2=j,b^a=bfg,c^a=cgh,d^a=dgj,d^b=dg,d^c=dj,e^a=ehij,e^c=ej,i^a=ij

Conjugacy classes & character table

136 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, 3, F.7*F.8*F.10);;
gap> SetPower(coll, 4, F.8);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);