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C₆₁×#62080 #29565513

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

2806 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 55068);