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D₉₈₄ #14520145

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

Aliases

Splittings

Subgroups

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 52 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);(2,8)(3,7)(4,6)(10,11)(13,52)(14,51)(15,50)(16,49)(17,48)(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:

2^4,3,41|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^40

Conjugacy classes & character table

495 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 68);