Finite Group Databasebeta

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#72250728

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

Aliases

No aliases for this group.

Subgroups

2719 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=i,b^2=h,c^2=h,d^2=eg,e^2=i,i^2=j,b^a=bf,d^b=de,d^c=di,e^a=ej,e^b=ei,e^c=ej,f^a=fj,f^d=fj,g^a=gj,h^d=hj,i^b=ij

Conjugacy classes & character table

130 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.9);;
gap> SetPower(coll, 2, F.8);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.5*F.7);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, 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);