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C₂₉×#2777 #16816491

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

378 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)(30,31,33,34)(32,35,36,37)(38,39)(40,41)(42,43)(44,45)(46,47,51,53)(48,50,49,52);(31,34)(32,36)(39,43)(41,44)(46,48,51,49)(47,52,53,50);(30,31)(32,35)(33,34)(36,37)(38,40)(39,44)(41,43)(42,45)(46,49,51,48)(47,52,53,50);(30,32,33,36)(31,35,34,37)(38,41,42,44)(39,40,43,45)(46,50,51,52)(47,48,53,49)

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, 1509);