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C₃₇×#3240 #17992058

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

328 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)(56,64)(57,63)(58,60)(59,62)(61,65)(66,69)(67,68);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51)(55,60)(61,68)(62,63)(64,69);(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52)(54,56,58,66)(55,61,60,68)(57,65,59,67)(62,64,63,69);(39,45)(43,46)(44,53)(51,52)(54,57,58,59)(55,62,60,63)(56,65,66,67)(61,64,68,69)

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, 1972);