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C₆₁×#62090 #29565523

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

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, 55078);