Finite Group Databasebeta

?

← Prev (#92214) Next (#92216) →

C₃⋊D₈₁ #92215

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

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 84 points:

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

Polycyclic presentation:

2,3^5|b^3=d^2e,d^3=e^2f,e^3=f^2,b^a=b^2d,c^a=c^2,d^a=d^2e,e^a=e^2f,f^a=f^2

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 60);