Finite Group Databasebeta

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C₂₉×#2824 #16816538

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

472 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)(38,39,41,42)(40,43,45,44)(46,47)(48,51)(49,50)(52,53);(32,36)(35,37)(39,42)(43,44)(47,50)(51,52);(30,31)(32,35)(33,34)(36,37)(38,39)(40,44)(41,42)(43,45)(46,48)(47,51)(49,53)(50,52);(30,32)(31,35)(33,36)(34,37)(38,40)(39,43)(41,45)(42,44)(46,47)(48,52)(49,50)(51,53)

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, 1556);