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#72343993

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

Aliases

No aliases for this group.

Subgroups

1400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,d^2=h,e^2=h,g^2=i,i^2=j,b^a=bi,c^a=cf,c^b=ch,d^a=dg,d^b=dg,d^c=dh,e^d=ej,g^a=gi,g^b=gij,g^d=gij,i^a=ij,i^b=ij,i^d=ij

Conjugacy classes & character table

100 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.5);;
gap> SetPower(coll, 4, F.8);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);