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C₂₉×#3356 #16817070

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

342 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)(30,31,34,33)(32,36,37,35)(38,39,41,45)(40,47,48,43)(42,44,50,46)(49,51,53,52);(30,32)(31,35)(33,36)(34,37)(38,40,41,48)(39,43,45,47)(42,49,50,53)(44,52,46,51);(30,33,34,31)(32,36,37,35)(39,44)(40,48)(42,50)(43,51)(45,46)(47,52);(32,37)(35,36)(39,45)(40,48)(44,46)(49,53)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2088);