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C₃₇×#1658 #17990476

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(39,44)(40,47)(41,42)(46,49)(48,50)(51,52)(55,59)(57,64)(60,68)(61,65)(62,66)(67,69);(38,39)(40,45)(41,49)(42,44)(43,46)(47,52)(48,53)(50,51)(54,55,58,61)(56,60,63,69)(57,65,64,59)(62,67,66,68);(38,40,43,48)(39,45,46,53)(41,47,42,50)(44,51,49,52)(54,56,58,63)(55,60,61,69)(57,66,64,62)(59,67,65,68)

Conjugacy classes & character table

740 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 390);