Finite Group Databasebeta

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#72257521

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

Aliases

No aliases for this group.

Subgroups

3326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=h,c^2=fi,d^2=ehij,e^2=i,i^2=j,c^a=cf,c^b=cfg,d^a=dfg,d^b=de,d^c=dij,e^b=ei,e^c=ej,e^d=ej,f^d=fj,g^c=gj,g^d=gj,h^d=hj,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.8);;
gap> SetPower(coll, 3, F.6*F.9);;
gap> SetPower(coll, 4, F.5*F.8*F.9*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, 1, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
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, 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> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);