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C₂₉×#3219 #16816933

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

396 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)(33,35)(34,37)(38,39)(40,48)(41,47)(42,44)(43,46)(45,49)(50,53)(51,52);(30,32,33,37)(31,34,35,36)(39,44)(45,52)(46,47)(48,53);(32,37)(34,36)(38,40)(39,45)(41,49)(42,50)(43,51)(44,52)(46,48)(47,53);(31,35)(34,36)(38,41,42,43)(39,46,44,47)(40,49,50,51)(45,48,52,53)

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, 1951);