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C₃₇×#2245 #17991063

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 77 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)(40,43)(41,42)(44,45)(46,47,53,59)(48,55,63,74)(49,54,65,72)(50,57,67,69)(51,56,60,75)(52,68,66,58)(61,73,76,71)(62,77,64,70);(39,42)(43,45)(46,48,60,76,52,62,50,49,53,63,51,61,66,64,67,65)(47,54,69,77,58,71,56,55,59,72,57,70,68,73,75,74);(38,40,41,44)(39,43,42,45)(46,49,50,64,66,76,60,63,53,65,67,62,52,61,51,48)(47,55,56,73,68,77,69,72,59,74,75,71,58,70,57,54)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 977);