Finite Group Databasebeta

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C₃×#87604 #11923973

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 100 points:

(1,2,3)(5,6,7,9)(8,11,12,18)(10,15,16,14)(13,20,21,31)(17,24,25,27)(19,28,29,23)(22,33,34,48)(26,37,38,44)(30,41,42,40)(32,45,46,36)(35,50,51,69)(39,54,55,65)(43,58,59,61)(47,62,63,57)(49,66,67,53)(52,71,72,89)(56,75,76,85)(60,79,80,83)(64,82,77,81)(68,84,73,78)(70,86,87,74)(88,93,94,92)(90,95,96,91)(97,99,100,98);(4,5,8,13,22,35,52,73,67,48,65,83,75,50,70,88,95,86,66,45,28,15,6,10,17,26,39,56,77,63,46,31,44,61,81,71,90,97,99,93,84,62,41,24,11,19,30,43,60,80,59,42,29,18,27,40,57,78,92,98,100,96,89,82,58,37,20,32,47,64,76,55,38,25,16,9,14,23,36,53,74,91,94,87,69,85,79,54,33,49,68,72,51,34,21,12,7)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1164, 9);