Finite Group Databasebeta

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C₂₉×#2810 #16816524

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 points:

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

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1542);