Finite Group Databasebeta

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D₈₁⋊C₃ #92189

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

Aliases

Splittings

Subgroups

23 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 81 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 34);