Finite Group Databasebeta

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#72234279

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

Aliases

No aliases for this group.

Subgroups

291 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 64 points:

(1,2)(3,12,14,22)(4,17)(5,19)(6,9)(7,11)(8,13,23,16)(10,21)(15,30,29,27)(18,25)(20,26)(24,31,32,28)(33,34,35,39,36,40,43,49,37,41,44,50,46,52,55,59,38,42,45,51,47,53,56,60,48,54,57,61,58,62,63,64);(1,3,5,15,6,16,20,31,7,14,21,29,4,13,18,28)(2,8,10,24,9,22,25,30,11,23,19,32,17,12,26,27);(1,4,7,6)(2,9,11,17)(3,13,14,16)(5,18,21,20)(8,22,23,12)(10,25,19,26)(15,28,29,31)(24,30,32,27)

Polycyclic presentation:

2^10|a^2=d,b^2=e,c^2=i,d^2=f,e^2=g,f^2=h,g^2=i,h^2=j,b^a=bgi,c^a=ci,d^b=di,e^a=ei

Conjugacy classes & character table

352 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.4);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);