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C₂₉×#2791 #16816505

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

360 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)(38,39)(40,44)(41,42)(43,45)(46,47,50,53)(48,52,49,51);(31,34)(35,37)(38,40,42,45)(39,43,41,44);(30,31,33,34)(32,35,36,37)(38,41,42,39)(40,43,45,44)(46,48,50,49)(47,51,53,52);(30,32,33,36)(31,35,34,37)(38,40)(39,44)(41,43)(42,45)(46,49,50,48)(47,52,53,51)

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, 1523);