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C₁₃×#4223 #14523819

• 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 54 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16,17,19)(18,21,22,28)(20,25,26,24)(23,30,31,41)(27,34,35,37)(29,38,39,33)(32,43,44,48)(36,46,47,53)(40,50,51,49)(42,54,52,45);(14,15,18,23,32,43,47,35,26,19,24,33,45,46,30,42,51,39,28,37,49,50,34,21,29,40,52,41,53,54,38,25,16,20,27,36,48,44,31,22,17)

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2132, 6);