Finite Group Databasebeta

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C₂₉×#3122 #16816836

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

418 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)(32,35)(33,34)(36,37)(38,39)(40,47)(41,45)(42,44)(43,48)(46,50)(49,52)(51,53);(31,34)(35,37)(38,40)(39,43)(41,48)(42,49)(44,51)(45,47)(46,52)(50,53);(39,44)(42,50)(43,51)(45,46)(47,52)(49,53);(30,32,33,36)(31,35,34,37)(40,48)(43,47)(49,53)(51,52)

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, 1854);