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C₂₉×#2787 #16816501

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

392 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)(32,36)(33,34)(35,37)(38,39,42,43)(40,44,45,41)(46,47,50,53)(48,51,52,49);(31,34)(32,37)(39,43)(41,44)(46,48,50,52)(47,51,53,49);(30,32)(31,35)(33,37)(34,36)(38,40)(39,41)(42,45)(43,44)(46,47)(48,51)(49,52)(50,53);(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,44)(43,45)(46,49,50,51)(47,52,53,48)

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, 1519);