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C₃₇×#3237 #17992055

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

322 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)(54,55,59,62)(56,63,64,69)(57,61,58,66)(60,67,68,65);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51)(56,64)(60,68)(63,69)(65,67);(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52)(54,56)(55,60)(57,65)(58,67)(59,64)(61,69)(62,68)(63,66);(39,45)(43,46)(44,53)(51,52)(54,57,59,58)(55,61,62,66)(56,65,64,67)(60,69,68,63)

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, 1969);