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C₃₇×#3196 #17992014

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

414 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)(40,44)(41,43)(42,45)(46,47)(48,52)(49,56)(50,59)(51,54)(53,55)(57,61)(58,60);(38,40)(39,42)(41,45)(43,44)(46,48,51,50)(47,52,54,59)(49,57,58,55)(53,56,61,60);(40,45)(42,44)(46,49,51,58)(47,53,54,61)(48,55,50,57)(52,60,59,56);(39,43)(42,44)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1928);