Finite Group Databasebeta

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C₂₉×#2030 #16815744

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(38,39)(40,43)(41,44)(42,45)(46,51)(47,50)(48,52)(49,53);(30,32,33,37)(31,34,35,36)(38,40)(39,43)(41,46)(42,47)(44,51)(45,50)(48,53)(49,52);(38,41,42,48)(39,44,45,52)(40,46,47,53)(43,49,50,51)

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, 762);