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#72224952

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

Aliases

No aliases for this group.

Subgroups

3373 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=f,c^2=e,g^2=ij,h^2=j,i^2=j,b^a=bh,c^b=cf,d^a=dg,d^b=df,d^c=de,f^a=fj,g^d=gi,h^a=hj,h^c=hj,h^d=hj,i^d=ij

Conjugacy classes & character table

94 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, 2, F.6);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);