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C₂₉×#3204 #16816918

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

402 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)(38,39,42,47)(40,49,51,44)(41,48,43,46)(45,52,53,50);(30,32)(31,34)(33,37)(35,36)(38,40,42,51)(39,44,47,49)(41,52,43,50)(45,46,53,48);(32,37)(34,36)(38,40)(39,45)(41,50)(42,51)(43,52)(44,48)(46,49)(47,53);(31,35)(34,36)(38,41,42,43)(39,46,47,48)(40,50,51,52)(44,45,49,53)

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, 1936);