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C₆₁×#62062 #29565495

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 101 points:

(2,5)(3,7)(9,10,15,19)(11,16,22,31)(12,23,25,33)(13,18,14,27)(17,28,34,24)(20,35,37,40)(21,30,26,32)(29,36,39,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2)(3,6)(4,5)(7,8)(9,11)(10,16)(12,20)(13,26)(14,21)(15,22)(17,29)(18,32)(19,31)(23,35)(24,38)(25,37)(27,30)(28,36)(33,40)(34,39);(9,12,15,25)(10,17,19,34)(11,20,22,37)(13,24,14,28)(16,29,31,39)(18,33,27,23)(21,36,26,38)(30,35,32,40);(2,5)(6,8)(9,13,15,14)(10,18,19,27)(11,21,22,26)(12,24,25,28)(16,30,31,32)(17,33,34,23)(20,36,37,38)(29,35,39,40);(1,3,4,7)(2,6,5,8)(11,22)(16,31)(20,37)(21,26)(29,39)(30,32)(35,40)(36,38)

Conjugacy classes & character table

3172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 55050);