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#72310946

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

Aliases

No aliases for this group.

Subgroups

2793 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=hj,c^2=gij,e^2=i,b^a=bh,c^a=cf,c^b=cfg,d^b=dgj,e^a=ei,e^b=eh,e^c=eh,e^d=efij,f^b=fi,f^c=fij,g^a=gij,g^b=gij,g^e=gj,h^c=hj,h^d=hij

Conjugacy classes & character table

61 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, 2, F.8*F.10);;
gap> SetPower(coll, 3, F.7*F.9*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*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, 5, 4, F.5*F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);