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C₃₇×#2821 #17991639

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 65 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)(42,43,45,47)(44,46,48,49)(51,55)(56,58)(57,61)(64,65);(39,41)(44,48)(46,49)(50,51)(52,58)(53,61)(54,55)(56,60)(57,63)(59,64)(62,65);(38,39)(40,41)(42,43)(44,46)(45,47)(48,49)(50,52,54,60)(51,56,55,58)(53,62,63,59)(57,65,61,64);(42,44)(43,46)(45,48)(47,49)(50,53,54,63)(51,57,55,61)(52,59,60,62)(56,64,58,65)

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, 1553);