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C₃₇×#3288 #17992106

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(39,44)(41,42)(45,52)(46,50)(47,53)(48,51);(38,39)(40,47)(41,50)(42,44)(43,46)(45,48)(49,52)(51,53);(38,39)(40,45)(41,44)(42,50)(43,46)(47,48)(49,53)(51,52);(38,40)(39,45)(41,51)(42,48)(43,49)(44,52)(46,53)(47,50)

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, 2020);