Finite Group Databasebeta

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#72321820

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

Aliases

No aliases for this group.

Subgroups

5487 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 44 points:

(1,2)(3,4)(13,14)(15,21)(16,22)(17,30)(18,24)(19,34)(20,27)(23,33)(25,37)(26,38)(28,43)(29,40)(31,39)(32,44)(35,41)(36,42);(5,6)(7,9)(8,10)(11,12)(13,15)(14,20)(16,28)(17,31)(18,26)(19,25)(21,30)(22,39)(23,37)(24,36)(27,33)(29,42)(32,41)(34,35)(38,44)(40,43);(5,6)(7,9)(8,10)(11,12)(13,15)(14,21)(16,25)(17,27)(18,26)(19,28)(20,30)(22,37)(23,39)(24,38)(29,41)(31,33)(32,42)(34,43)(35,40)(36,44);(5,7,8,11)(6,9,10,12)(13,16,18,19)(14,22,24,34)(15,25,26,28)(17,29,32,33)(20,35,36,39)(21,37,38,43)(23,30,40,44)(27,41,42,31);(2,4)(6,10)(7,11)(15,26)(20,36)(21,38)(25,28)(27,42)(31,41)(35,39)(37,43)

Polycyclic presentation:

2^10|d^2=h,g^2=ij,i^2=j,b^a=bg,d^b=dj,e^a=ef,e^b=eh,e^c=eh,e^d=ehj,g^a=gi,g^b=gi,i^a=ij,i^b=ij

Conjugacy classes & character table

124 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, 4, F.8);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);