Finite Group Databasebeta

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C₃₇×#368 #14557033

• nilpotent
• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 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)(38,39,42,47,44,48,43,58)(40,49,52,64,54,65,53,68)(41,55,56,62,57,69,50,46)(45,59,60,67,61,66,63,51);(38,40,50,66,43,53,57,67,44,54,56,59,42,52,41,51)(39,45,55,64,47,60,62,65,48,61,69,68,58,63,46,49)

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, 49);