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C₃₇×#3204 #17992022

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

402 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)(46,47,50,55)(48,57,59,52)(49,56,51,54)(53,60,61,58);(38,40)(39,42)(41,45)(43,44)(46,48,50,59)(47,52,55,57)(49,60,51,58)(53,54,61,56);(40,45)(42,44)(46,48)(47,53)(49,58)(50,59)(51,60)(52,56)(54,57)(55,61);(39,43)(42,44)(46,49,50,51)(47,54,55,56)(48,58,59,60)(52,53,57,61)

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, 1936);