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C₂×C₃₇×#548 #17992283

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 51 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(4,6)(8,11)(12,13);(7,8,10,11)(9,13,14,12);(3,4)(5,6);(7,9,10,14)(8,12,11,13)

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2197);