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D₇₄₇ #13093643

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

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 92 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92);(2,9)(3,8)(4,7)(5,6)(11,92)(12,91)(13,90)(14,89)(15,88)(16,87)(17,86)(18,85)(19,84)(20,83)(21,82)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Polycyclic presentation:

2,3,83,3|b^3=d^2,b^a=b^2d,c^a=c^82,d^a=d^2

Conjugacy classes & character table

375 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1494, 3);