Finite Group Databasebeta

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C₂₉×#3234 #16816948

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

368 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)(32,36)(35,37)(38,39)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53);(31,35)(34,37)(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51);(30,31)(32,37)(33,35)(34,36)(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52);(39,45)(43,46)(44,53)(51,52)

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, 1966);