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C₃₇×#3502 #17992320

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

964 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)(38,39,41,43)(40,44,45,42)(46,47,51,55)(48,53,49,52)(50,54,58,61)(56,60,57,59);(46,48,51,49)(47,52,55,53)(50,57,58,56)(54,60,61,59);(38,40,41,45)(39,42,43,44)(46,49,51,48)(47,53,55,52)(50,57,58,56)(54,60,61,59);(46,50,51,58)(47,54,55,61)(48,56,49,57)(52,59,53,60);(46,47)(48,52)(49,53)(50,54)(51,55)(56,59)(57,60)(58,61)

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, 2234);