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#72233052

• p-group
• nilpotent
• supersolvable
• solvable
• monomial
• stem
• rational
• ambivalent

Aliases

No aliases for this group.

Subgroups

At least 12336 conjugacy classes of subgroups; only the 784 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(3,7)(9,10)(11,14)(12,16)(13,15)(17,22)(18,24)(19,21)(20,23);(2,5)(3,7)(6,8)(9,11)(10,14)(12,19,20,18)(13,17)(15,22)(16,24,23,21);(2,6)(5,8)(10,15)(11,17);(1,2)(3,6)(4,5)(7,8)(9,12)(10,16)(11,18)(13,20)(14,21)(15,23)(17,19)(22,24);(11,17)(14,22)(18,19)(21,24)

Polycyclic presentation:

2^11|b^2=h,b^a=bh,c^a=chij,c^b=chij,d^a=dg,d^b=dgk,d^c=df,e^b=eij,f^a=fi,f^b=fi,g^b=gij,g^c=gjk,g^f=gk,h^d=hij,i^d=ik,j^d=jk

Conjugacy classes & character table

125 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, 2, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.11);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10*F.11);;
gap> SetConjugate(coll, 7, 6, F.7*F.11);;
gap> SetConjugate(coll, 8, 4, F.8*F.9*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.11);;
gap> SetConjugate(coll, 10, 4, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);