Finite Group Databasebeta

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#72257493

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

Aliases

No aliases for this group.

Subgroups

1792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=h,c^2=gij,d^2=eghi,e^2=i,i^2=j,c^a=cf,c^b=cfg,d^a=dgj,d^b=de,d^c=degi,e^b=ei,e^c=ei,e^d=ej,f^d=fj,g^c=gj,h^d=hj,i^b=ij,i^c=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.8);;
gap> SetPower(coll, 3, F.7*F.9*F.10);;
gap> SetPower(coll, 4, F.5*F.7*F.8*F.9);;
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, 1, F.4*F.7*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.7*F.9);;
gap> SetConjugate(coll, 5, 2, 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, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, 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);