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#72340028

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

Aliases

No aliases for this group.

Subgroups

829720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

(2,4)(5,6,8,7)(10,11)(13,14)(15,17)(16,19)(18,20)(23,27)(25,28);(21,22,24,26)(23,25,27,28);(2,4)(6,7)(9,10,12,11)(14,15)(16,20)(21,22)(23,28)(24,26)(25,27);(1,2,3,4)(5,7,8,6)(9,11,12,10)(13,15,17,14)(16,18,20,19)(21,22)(23,28)(24,26)(25,27);(21,23)(22,25)(24,27)(26,28);(13,16)(14,18)(15,19)(17,20)(21,23)(22,25)(24,27)(26,28)

Polycyclic presentation:

2^11|a^2=g,b^2=h,c^2=ghik,d^2=ghj,c^a=chi,c^b=ch,d^a=dhj,d^b=dh,d^c=dijk,e^a=eh,e^c=eh,e^d=eh,f^a=fhk,f^c=fhk,f^d=fhk

Conjugacy classes & character table

320 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.7);;
gap> SetPower(coll, 2, F.8);;
gap> SetPower(coll, 3, F.7*F.8*F.9*F.11);;
gap> SetPower(coll, 4, F.7*F.8*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10*F.11);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.11);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.11);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);