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#72285409

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

Aliases

No aliases for this group.

Subgroups

3672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,d^2=hij,f^2=ij,h^2=j,d^a=df,d^b=de,d^c=dij,f^a=fh,f^c=fj,g^d=ghi,g^f=gij,h^a=hi,h^g=hj,i^a=ij

Conjugacy classes & character table

73 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, 4, F.8*F.9*F.10);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.8*F.9);;
gap> SetConjugate(coll, 7, 6, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 7, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);