Finite Group Databasebeta

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#72280451

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

Aliases

No aliases for this group.

Subgroups

3583 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=e,d^2=fg,f^2=ij,i^2=j,c^a=ch,d^a=dh,d^b=df,d^c=dfg,e^d=ej,f^b=fi,f^c=fij,g^a=gj,g^b=gj,h^d=hj,i^b=ij,i^c=ij

Conjugacy classes & character table

106 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, 3, F.5);;
gap> SetPower(coll, 4, F.6*F.7);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.7);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 2, 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);