Finite Group Databasebeta

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#72321776

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

Aliases

No aliases for this group.

Subgroups

2406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 48 points:

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

Polycyclic presentation:

2^10|c^2=fh,e^2=fgi,f^2=hj,g^2=i,h^2=j,c^a=cf,c^b=cij,d^b=dj,e^a=efh,e^c=ej,f^a=fh,h^a=hj

Conjugacy classes & character table

148 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, 3, F.6*F.8);;
gap> SetPower(coll, 5, F.6*F.7*F.9);;
gap> SetPower(coll, 6, F.8*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.6*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);