Finite Group Databasebeta

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#72225392

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

Aliases

No aliases for this group.

Subgroups

1798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|b^2=e,c^2=f,d^2=gik,f^2=h,g^2=i,h^2=j,i^2=k,b^a=bk,c^a=cg,c^b=cj,d^a=dg,d^b=dk,f^a=fi,g^a=gik,h^a=hk,i^a=ik

Conjugacy classes & character table

344 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7*F.9*F.11);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.11);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.11);;
gap> SetConjugate(coll, 8, 1, F.8*F.11);;
gap> SetConjugate(coll, 9, 1, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);