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D₂₀₀ #87714

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

Aliases

Splittings

Subgroups

33 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 33 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);(2,8)(3,7)(4,6)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

Polycyclic presentation:

2^4,5^2|b^2=cd,c^2=d,e^5=f^4,b^a=bc,c^a=cd,e^a=e^4f,f^a=f^4

Conjugacy classes & character table

103 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 8);