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C₃₇×#3523 #17992341

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

992 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)(39,42)(43,45)(46,47,51,49)(48,54,56,52)(50,57,58,53)(55,59,61,60);(46,48,51,56)(47,52,49,54)(50,55,58,61)(53,59,57,60);(38,39)(40,43)(41,42)(44,45);(46,49,51,47)(48,52,56,54)(50,57,58,53)(55,59,61,60);(38,40,41,44)(39,43,42,45)(46,50,51,58)(47,53,49,57)(48,55,56,61)(52,59,54,60)

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, 2255);