Finite Group Databasebeta

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#72225209

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

Aliases

No aliases for this group.

Subgroups

1329 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 48 points:

(1,2,4,7,5,8,13,15,6,9,14,3,10,11,16,12)(18,23,24,27,26,37,39,44)(19,28,29,31)(20,32)(25,40,41,48,42,43,38,36)(30,47,46,35)(33,45);(17,18,19,25,20,27,30,43,21,24,31,38,33,37,47,48,22,26,29,42,32,44,46,40,34,39,28,41,45,23,35,36);(1,3,4,8,5,12,13,9,6,7,14,11,10,15,16,2)

Polycyclic presentation:

2^12|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,f^2=i,g^2=k,h^2=j,i^2=k,j^2=l,b^a=bhjl,c^a=cik,d^b=djl,d^c=dk,e^a=ejl,e^d=el,f^a=fk,g^b=gl,h^a=hl

Conjugacy classes & character table

352 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", "k", "l");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.4);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 7, F.11);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetPower(coll, 10, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.10*F.12);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.11);;
gap> SetConjugate(coll, 4, 2, F.4*F.10*F.12);;
gap> SetConjugate(coll, 4, 3, F.4*F.11);;
gap> SetConjugate(coll, 5, 1, F.5*F.10*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.12);;
gap> SetConjugate(coll, 6, 1, F.6*F.11);;
gap> SetConjugate(coll, 7, 2, F.7*F.12);;
gap> SetConjugate(coll, 8, 1, F.8*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);