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C₂×C₃₇×#433 #17991737

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 63 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63);(3,4)(5,8)(6,7)(9,10)(11,12,14,17,15,18,21,24)(13,16,20,23,19,22,25,26);(4,7)(8,10)(11,13)(12,16)(14,20)(15,19)(17,23)(18,22)(21,25)(24,26);(3,5,6,9)(4,8,7,10)(13,19)(16,22)(20,25)(23,26)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1651);