Finite Group Databasebeta

?

← Prev (#14520353) Next (#14520355) →

Dic₄₉₄ #14520354

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 40 points:

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

Polycyclic presentation:

2^3,13,19|a^2=c,b^2=c,b^a=bc,d^a=d^12,e^a=e^18

Conjugacy classes & character table

497 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1976, 24);