Finite Group Databasebeta

?

← Prev (#92609) Next (#92611) →

D₂₅₂ #92610

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

Aliases

Splittings

Subgroups

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20);(2,4)(6,13)(7,12)(8,11)(9,10)(15,20)(16,19)(17,18)

Polycyclic presentation:

2^3,3,7,3|b^2=c,d^3=f^2,b^a=bc,d^a=d^2f,e^a=e^6,f^a=f^2

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 36);