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C₂₉×#2821 #16816535

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 57 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)(34,35,37,39)(36,38,40,41)(43,47)(48,50)(49,53)(56,57);(31,33)(36,40)(38,41)(42,43)(44,50)(45,53)(46,47)(48,52)(49,55)(51,56)(54,57);(30,31)(32,33)(34,35)(36,38)(37,39)(40,41)(42,44,46,52)(43,48,47,50)(45,54,55,51)(49,57,53,56);(34,36)(35,38)(37,40)(39,41)(42,45,46,55)(43,49,47,53)(44,51,52,54)(48,56,50,57)

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, 1553);