Finite Group Databasebeta

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C₂₉×#2842 #16816556

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

548 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)(31,34)(35,37)(38,39)(40,42)(41,43)(44,45)(48,52)(50,53);(32,36)(35,37)(39,40)(43,44)(46,47,49,51)(48,53,52,50);(30,31)(32,35)(33,34)(36,37)(38,40,42,39)(41,43,45,44)(46,48,49,52)(47,50,51,53);(30,32)(31,35)(33,36)(34,37)(38,41)(39,43)(40,44)(42,45)(46,47)(48,50)(49,51)(52,53)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1574);