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C₃₇×#473 #14557138

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

100 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)(38,39,44,49)(40,50,54,60)(41,55,57,63)(42,48,43,47)(45,53,61,52)(46,58,62,56)(51,65,67,59)(64,68,69,66);(38,40,43,53,44,54,42,52)(39,45,48,60,49,61,47,50)(41,51,58,68,57,67,56,66)(46,59,63,69,62,65,55,64);(38,41)(39,46)(40,51)(42,56)(43,58)(44,57)(45,59)(47,55)(48,63)(49,62)(50,64)(52,66)(53,68)(54,67)(60,69)(61,65)

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 154);