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C₅₉×#563 #16837097

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)(61,64)(62,66)(68,69,73,71)(70,76,78,74)(72,79,81,75)(77,82,80,83);(61,64)(65,67)(68,70,73,78)(69,74,71,76)(72,80,81,77)(75,83,79,82);(60,61)(62,65)(63,64)(66,67)(68,71,73,69)(70,74,78,76)(72,79,81,75)(77,82,80,83);(60,62)(61,65)(63,66)(64,67)(68,72)(69,75)(70,77)(71,79)(73,81)(74,82)(76,83)(78,80)

Conjugacy classes & character table

1121 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 244);