Finite Group Databasebeta

?

← Prev (#16864682) Next (#16864684) →

Dic₁₀₈₅ #16864683

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 47 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);(1,3,2,4)(6,9)(7,8)(11,16)(12,15)(13,14)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

Polycyclic presentation:

2,5,7,31,2|a^2=e,b^a=b^4,c^a=c^6,d^a=d^30

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4340, 9);