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C₆₁×#62069 #29565502

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55057);