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C₂₉×#2767 #16816481

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

344 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)(40,43)(41,45)(47,50)(48,52);(31,33)(32,37)(38,39,42,44)(40,41,43,45)(46,47,49,50)(48,53,52,51);(30,32,34,37)(31,35,33,36)(38,40,42,43)(39,41,44,45);(30,33,34,31)(32,36,37,35)(38,41)(39,43)(40,44)(42,45)(46,48,49,52)(47,51,50,53)

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, 1499);