Finite Group Databasebeta

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#72250340

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

Aliases

No aliases for this group.

Subgroups

1661 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=h,c^2=gi,d^2=eghj,e^2=i,i^2=j,c^a=cf,c^b=cfg,d^b=de,d^c=degh,e^b=ei,e^c=eij,g^c=gj,g^d=gj,h^d=hj,i^b=ij,i^c=ij

Conjugacy classes & character table

100 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.8);;
gap> SetPower(coll, 3, F.7*F.9);;
gap> SetPower(coll, 4, F.5*F.7*F.8*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.7*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*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);