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C₃×#4223 #92449

• 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 44 points:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(492, 5);