Finite Group Databasebeta

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#72224809

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

Aliases

No aliases for this group.

Subgroups

2773 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,e^2=h,g^2=ij,i^2=j,c^a=cg,c^b=ce,d^a=dj,d^b=dj,e^a=ei,e^b=eh,e^c=eh,g^a=gi,g^b=gi,g^c=gi,h^a=hj,i^a=ij,i^b=ij,i^c=ij

Conjugacy classes & character table

112 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.6);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);