Finite Group Databasebeta

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#72328945

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

Aliases

No aliases for this group.

Subgroups

At least 6824 conjugacy classes of subgroups; only the 929 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Polycyclic presentation:

2^10|a^2=j,b^2=h,d^2=h,e^2=gij,b^a=bg,c^b=cf,d^a=dhj,d^c=dhi,e^a=efghj,e^b=efghi,e^c=efhij,e^d=efghi

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

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