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C₃₇×#3480 #17992298

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 53 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)(46,47,50,52)(48,51,49,53);(38,39)(40,43)(41,42)(44,45)(46,48,50,49)(47,51,52,53);(46,49,50,48)(47,51,52,53);(39,42)(43,45);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2212);