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C₃₇×#3461 #17992279

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(40,43)(41,42)(44,45)(46,47)(48,54)(49,52)(50,53)(51,56)(55,60)(57,59)(58,61);(46,48,50,56)(47,51,53,54)(49,57,58,55)(52,60,61,59);(39,42)(43,45)(46,49,50,58)(47,52,53,61)(48,55,56,57)(51,59,54,60);(47,53)(51,54)(52,61)(59,60);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2193);