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C₃₇×#3179 #17991997

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

374 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)(40,43)(41,42)(44,45)(46,47,51,54)(48,52,56,60)(49,58,53,50)(55,57,59,61);(39,42)(43,45)(46,48)(47,52)(49,59)(50,57)(51,56)(53,55)(54,60)(58,61);(46,49,50,47,51,53,58,54)(48,55,57,60,56,59,61,52);(38,40,41,44)(39,43,42,45)(48,56)(52,60)(55,59)(57,61)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1911);