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C₃⋊#19151048 #30685196

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

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 89 points:

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

Polycyclic presentation:

2,3^2,13,73|c^a=c^2,d^a=d^12,e^a=e^72,d^b=d^3,e^b=e^64

Conjugacy classes & character table

483 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17082, 58);