Finite Group Databasebeta

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#72320515

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

Aliases

No aliases for this group.

Subgroups

2108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,d^2=ij,h^2=i,i^2=j,b^a=bh,c^a=cf,c^b=cg,d^a=di,d^b=dfg,d^c=dej,e^b=ej,g^d=gj,h^a=hi,h^b=hij,h^d=hj,i^a=ij,i^b=ij

Conjugacy classes & character table

82 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, 1, F.5);;
gap> SetPower(coll, 4, F.9*F.10);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);