Finite Group Databasebeta

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C₃₇×#578 #14557243

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

248 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)(38,39,43,47)(40,48,51,61)(41,45,52,59)(42,54,56,46)(44,55,58,50)(49,62,63,69)(53,66,65,60)(57,67,68,64);(38,40,43,51)(39,44,47,58)(41,49,52,63)(42,55,56,50)(45,57,59,68)(46,61,54,48)(53,67,65,64)(60,69,66,62);(38,41)(39,45)(40,49)(42,53)(43,52)(44,57)(46,60)(47,59)(48,62)(50,64)(51,63)(54,66)(55,67)(56,65)(58,68)(61,69);(41,52)(45,59)(49,63)(53,65)(57,68)(60,66)(62,69)(64,67)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 259);