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#72339976

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

Aliases

No aliases for this group.

Subgroups

828880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=g,b^2=gh,c^2=k,d^2=ghi,b^a=bh,c^a=cj,c^b=cj,d^a=dhi,d^b=dghi,d^c=djk,e^a=ehijk,e^b=ehijk,e^d=ehijk,f^a=fghk,f^b=fghk,f^d=fghk

Conjugacy classes & character table

296 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.7*F.8);;
gap> SetPower(coll, 3, F.11);;
gap> SetPower(coll, 4, F.7*F.8*F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.10*F.11);;
gap> SetConjugate(coll, 5, 1, F.5*F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 6, 1, F.6*F.7*F.8*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.7*F.8*F.11);;
gap> SetConjugate(coll, 6, 4, F.6*F.7*F.8*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);