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C₂×C₃₇×#536 #17992265

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 59 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(4,6)(8,12)(9,15)(10,18)(20,22);(7,8,11,12)(9,16,15,13)(10,14,18,19)(17,22,21,20);(3,4)(5,6)(7,9,11,15)(8,13,12,16)(10,17,18,21)(14,20,19,22);(7,10)(8,14)(9,17)(11,18)(12,19)(13,20)(15,21)(16,22)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2179);