Finite Group Databasebeta

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C₃⋊#19151044 #30685198

• 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:

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

Conjugacy classes & character table

519 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17082, 60);