Finite Group Databasebeta

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C₂₉×#3296 #16817010

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

408 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)(38,39)(40,43)(41,44)(42,46)(45,49)(47,50)(48,52)(51,53);(30,32)(31,34)(33,37)(35,36)(38,40,42,48)(39,43,46,52)(41,47,49,53)(44,50,45,51);(39,44)(41,49)(43,50)(45,46)(47,53)(51,52);(32,37)(34,36)

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2028);