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C₃₇×#3219 #17992037

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 61 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)(40,44)(41,43)(42,45)(46,47)(48,56)(49,55)(50,52)(51,54)(53,57)(58,61)(59,60);(38,40,41,45)(39,42,43,44)(47,52)(53,60)(54,55)(56,61);(40,45)(42,44)(46,48)(47,53)(49,57)(50,58)(51,59)(52,60)(54,56)(55,61);(39,43)(42,44)(46,49,50,51)(47,54,52,55)(48,57,58,59)(53,56,60,61)

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, 1951);