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#72233102

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

Aliases

No aliases for this group.

Subgroups

At least 7685 conjugacy classes of subgroups; only the 266 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 32 points:

(2,7)(3,11)(8,24)(9,22)(10,23)(12,28)(13,29)(14,30)(18,31)(20,27)(21,25)(26,32);(2,7,9,22)(4,15)(8,21,25,24)(10,23,18,31)(12,29)(13,28)(16,17)(20,27,32,26);(2,8)(4,16)(7,20)(9,25)(10,26)(12,13)(15,17)(18,27)(21,23)(22,32)(24,31)(28,29);(1,2)(3,8)(4,7)(5,18)(6,10)(9,19)(11,27)(12,20)(13,21)(14,26)(15,22)(16,23)(17,31)(24,28)(25,30)(29,32)

Polycyclic presentation:

2^11|b^2=g,b^a=bg,c^a=cgjk,c^b=cjk,d^a=df,d^b=dh,d^c=de,e^a=ei,f^b=fij,f^c=fj,f^e=fk,g^d=gij,h^b=hij,h^c=hk,i^d=ik,j^d=jk

Conjugacy classes & character table

95 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.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.10*F.11);;
gap> SetConjugate(coll, 3, 2, F.3*F.10*F.11);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.11);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.11);;
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);