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C₂₉×#2746 #16816460

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 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)(33,34)(35,37)(38,39,42,44)(40,45,41,43)(46,47)(48,51)(49,53)(50,52);(31,34)(35,36)(38,40,42,41)(39,43,44,45)(46,48,50,53)(47,51,52,49);(30,32,33,37)(31,35,34,36)(38,41,42,40)(39,43,44,45)(46,48)(47,49)(50,53)(51,52);(30,31)(32,35)(33,34)(36,37)(38,39)(40,45)(41,43)(42,44)(46,49)(47,48)(50,51)(52,53)

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, 1478);