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D₂₄₈ #92471

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

Aliases

Splittings

Subgroups

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 39 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);(2,8)(3,7)(4,6)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Polycyclic presentation:

2^4,31|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^30

Conjugacy classes & character table

127 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 6);