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C₂₉×#2745 #16816459

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

400 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)(32,34)(33,35)(36,37)(38,39)(40,43)(41,45)(42,44)(46,47,50,48)(49,52,53,51);(31,32)(33,37)(38,40,42,45)(39,43,44,41)(46,48,50,47)(49,52,53,51);(30,32,34,31)(33,36,37,35)(38,40)(39,41)(42,45)(43,44)(46,49)(47,51)(48,52)(50,53);(30,33)(31,35)(32,36)(34,37)(38,41)(39,40)(42,43)(44,45)(46,49)(47,51)(48,52)(50,53)

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, 1477);