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C₃₇×#3216 #17992034

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

390 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)(46,47,51,54)(48,55,56,61)(49,53,50,58)(52,59,60,57);(38,40,41,45)(39,42,43,44)(48,56)(52,60)(55,61)(57,59);(40,45)(42,44)(46,48)(47,52)(49,57)(50,59)(51,56)(53,61)(54,60)(55,58);(39,43)(42,44)(46,49,51,50)(47,53,54,58)(48,57,56,59)(52,61,60,55)

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, 1948);