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#72249885

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

Aliases

No aliases for this group.

Subgroups

2395 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,c^2=g,d^2=ehij,h^2=i,i^2=j,c^a=ce,c^b=cg,d^a=dehij,d^b=df,d^c=deij,f^c=fj,g^d=gj,h^a=hi,h^c=hj,i^a=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, 1, F.7);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.5*F.8*F.9*F.10);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);