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C₂₉×#2845 #16816559

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

340 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)(32,34,36,37)(38,39,42,41)(40,43,44,45)(47,50)(51,52);(32,36)(34,37)(39,41)(43,45)(46,47,49,50)(48,51,53,52);(30,31)(32,34)(33,35)(36,37)(38,40,42,44)(39,43,41,45)(46,47)(48,52)(49,50)(51,53);(30,32)(31,34)(33,36)(35,37)(38,41,42,39)(40,43,44,45)(46,48,49,53)(47,51,50,52)

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, 1577);