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C₂₉×#2743 #16816457

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 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)(30,31,34,32)(33,36,37,35)(38,39)(40,41)(42,43)(44,45)(46,47)(48,51)(49,53)(50,52);(31,32)(33,37)(39,43)(41,45)(46,48,50,53)(47,51,52,49);(30,32,34,31)(33,36,37,35)(38,40,42,44)(39,41,43,45)(46,48)(47,49)(50,53)(51,52);(30,33)(31,35)(32,36)(34,37)(38,41)(39,44)(40,43)(42,45)(46,49)(47,48)(50,51)(52,53)

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, 1475);