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C₃₇×#1425 #17990243

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

Aliases

Subgroups

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 101 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)(38,39,42,48,45,50,44,66)(40,51,54,76,57,78,56,88)(41,58,60,89,62,91,61,92)(43,64,63,74,65,93,59,49)(46,67,68,84,70,83,94,53)(47,71,72,81,73,80,90,52)(55,86,85,98,87,101,82,77)(69,79,75,95,96,100,97,99);(38,40,52,79,43,55,60,67,42,54,71,95,63,85,62,84,45,57,81,100,65,87,61,83,44,56,80,99,59,82,41,53)(39,46,58,77,49,69,90,88,66,94,92,101,93,97,73,78,50,70,91,98,74,96,72,76,48,68,89,86,64,75,47,51)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 157);