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C₅₃×#737 #16864301

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 80 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55,58)(56,60,66)(57,61,65)(59,67,64)(62,69,74)(63,70,73)(68,75,72)(71,77,79)(76,80,78);(55,59,61)(58,65,67)(60,68,70)(66,73,75)(69,76,77)(74,79,80);(54,56,62,57,63,71,64,72,78)(55,60,69,61,70,77,59,68,76)(58,66,74,65,73,79,67,75,80)

Conjugacy classes & character table

1749 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4293, 14);