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C₂×C₄₉⋊C₃ #64413

• 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 51 points:

(1,2)(4,6,10)(5,9,18)(7,13,25)(8,16,31)(11,22,20)(12,23,34)(14,27,45)(15,21,17)(19,36,35)(24,42,47)(26,44,37)(28,33,46)(29,39,40)(30,41,43)(32,48,38)(49,50,51);(3,33,16,44,41,26,49,5,34,7,51,31,20,27,9,25,15,11,28,38,22,19,43,30,24,13,40,39,18,4,46,32,10,50,42,35,8,6,14,21,47,37,36,17,12,29,23,45,48)

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 2);