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C₂₉×#2836 #16816550

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

358 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)(31,34)(35,37)(38,39,42,41)(40,43,44,45)(46,47)(48,52)(49,53)(50,51);(32,36)(35,37)(39,41)(40,44)(47,51)(49,52);(30,31,33,34)(32,35,36,37)(38,40)(39,43)(41,45)(42,44)(46,48)(47,52)(49,51)(50,53);(30,32)(31,35)(33,36)(34,37)(38,41,42,39)(40,43,44,45)(46,49,50,52)(47,53,51,48)

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, 1568);