Finite Group Databasebeta

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#72322327

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

Aliases

No aliases for this group.

Subgroups

1975 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=e,c^2=i,d^2=f,e^2=j,h^2=ij,i^2=j,b^a=bh,c^a=cg,c^b=cg,d^a=df,d^b=dfg,d^c=defi,e^a=ej,g^c=gj,h^a=hi,h^b=hij,i^a=ij,i^b=ij

Conjugacy classes & character table

88 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.5);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 8, F.9*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.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.6*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);