Finite Group Databasebeta

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#72286838

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

Aliases

No aliases for this group.

Subgroups

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=d,c^2=degh,d^2=f,e^2=g,f^2=h,g^2=i,h^2=j,i^2=j,b^a=bj,c^a=ce,d^c=dg,e^a=eij,e^c=eg,e^d=ej,f^c=fi,g^a=gj,g^c=gi,h^c=hj,i^c=ij

Conjugacy classes & character table

136 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.4);;
gap> SetPower(coll, 3, F.4*F.5*F.7*F.8);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.7);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);