Finite Group Databasebeta

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C₂₉×#3082 #16816796

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

362 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)(30,31,33,35)(32,36,37,34)(40,46)(41,48)(43,50)(45,52)(47,49)(51,53);(30,32,33,37)(31,34,35,36)(38,39)(40,43)(41,45)(42,44)(46,50)(47,51)(48,52)(49,53);(38,40,42,47)(39,43,44,51)(41,49,48,46)(45,53,52,50);(39,44)(43,51)(45,52)(50,53)

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, 1814);