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C₃×#87938 #11925916

• 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 104 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)(35,50,51,68)(39,54,55,65)(43,58,59,61)(47,62,63,57)(49,52,66,53)(56,69,70,83)(60,73,74,80)(64,77,78,76)(67,71,81,72)(75,84,85,94)(79,88,89,91)(82,86,92,87)(90,95,96,101)(93,97,99,98)(100,102,103,104);(4,5,8,13,22,35,52,45,28,15,6,10,17,26,39,56,71,62,41,24,11,19,30,43,60,75,86,77,58,37,20,32,47,64,79,90,97,88,73,54,33,49,67,82,93,100,102,95,84,69,50,68,83,94,101,104,103,99,92,81,66,48,65,80,91,98,96,89,78,63,46,31,44,61,76,87,85,74,59,42,29,18,27,40,57,72,70,55,38,25,16,9,14,23,36,53,51,34,21,12,7)

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1212, 5);