Finite Group Databasebeta

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#72234283

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

Aliases

No aliases for this group.

Subgroups

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 96 points:

(1,2,3,7,4,8,11,17,5,9,12,18,14,20,23,27,6,10,13,19,15,21,24,28,16,22,25,29,26,30,31,32)(33,34,36,41)(35,45,46,69,48,72,73,94)(37,43,52,63)(38,42,53,65)(39,44,51,64)(40,57,58,84,60,85,88,77)(47,71,74,87,76,59,86,61)(49,70,50,78,75,95,79,93)(54,67,81,62)(55,66,82,91)(56,68,80,90)(83,92,96,89);(33,35)(34,40,42,59,44,60,67,71)(36,50,51,79)(37,47)(38,49)(39,48)(41,61,62,58,64,87,65,88)(43,45,66,70,68,72,92,95)(46,53,73,81)(52,57,80,85)(54,75)(55,77)(56,76)(63,78,89,69,90,93,91,94)(74,82,86,96)(83,84)

Polycyclic presentation:

2^11|a^2=c,b^2=d,c^2=f,d^2=g,e^2=hj,f^2=i,h^2=j,i^2=k,b^a=be,c^b=ch,d^a=dhj,d^c=dj,f^b=fj,g^a=gj

Conjugacy classes & character table

368 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8*F.10);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);