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C₃₇×#3241 #17992059

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 69 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)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53)(54,55)(56,59)(57,60)(58,62)(61,65)(63,67)(64,66)(68,69);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51)(54,56)(55,59)(57,64)(58,63)(60,66)(61,68)(62,67)(65,69);(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52)(55,60)(57,65)(59,66)(61,62)(64,69)(67,68);(39,45)(43,46)(44,53)(51,52)(56,63)(59,67)(64,69)(66,68)

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, 1973);