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C₆₁×#62072 #29565505

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1780 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)(11,20,23,16)(12,25,27,32)(13,18,15,28)(17,29,33,26)(21,36,38,40)(22,35,24,31)(30,37,34,39)(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)(10,16)(12,21)(13,22)(14,23)(15,24)(17,30)(18,31)(19,20)(25,40)(26,37)(27,38)(28,35)(29,39)(32,36)(33,34);(9,12,14,27)(10,17,19,33)(11,21,23,38)(13,26,15,29)(16,30,20,34)(18,32,28,25)(22,37,24,39)(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, 55060);