Finite Group Databasebeta

?

← Prev (#72257158) Next (#72257160) →

#72257159

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

Aliases

No aliases for this group.

Subgroups

5724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,d^2=efi,e^2=ij,f^2=j,i^2=j,b^a=bh,c^a=cfhij,d^a=de,d^b=dg,d^c=defgj,e^a=ei,e^c=ei,f^c=fj,g^a=gj,h^d=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.6);;
gap> SetPower(coll, 4, F.5*F.6*F.9);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.6*F.7*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, 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);