Finite Group Databasebeta

?

← Prev (#72292008) Next (#72292010) →

Dic₁₄₈₀₅ #72292009

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18)(19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,18)(16,17)(20,25)(21,24)(22,23)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Polycyclic presentation:

2^2,3,5,7,47,3|a^2=b,c^3=g,c^a=c^2g^2,d^a=d^4,e^a=e^6,f^a=f^46,g^a=g^2

Conjugacy classes & character table

14808 conjugacy classes. The character table is too large to display.

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");;
gap> coll := SingleCollector(F, [2, 2, 3, 5, 7, 47, 3]);;
gap> SetPower(coll, 1, F.2);;
gap> SetPower(coll, 3, F.7);;
gap> SetConjugate(coll, 3, 1, F.3^2*F.7^2);;
gap> SetConjugate(coll, 4, 1, F.4^4);;
gap> SetConjugate(coll, 5, 1, F.5^6);;
gap> SetConjugate(coll, 6, 1, F.6^46);;
gap> SetConjugate(coll, 7, 1, F.7^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);