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#72257266

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

Aliases

No aliases for this group.

Subgroups

3625 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=j,d^2=fgi,e^2=ij,i^2=j,b^a=bg,c^a=ce,d^a=dgj,d^b=dh,d^c=df,e^a=ei,e^c=ei,f^d=fj,g^d=gj,h^a=hj,i^a=ij,i^c=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.10);;
gap> SetPower(coll, 4, F.6*F.7*F.9);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);