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C₆₁×#62091 #29565524

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(2,5)(3,7)(9,10)(11,21)(12,26)(13,20)(14,19)(15,18)(16,24)(17,27)(22,36)(23,31)(25,32)(28,34)(29,33)(30,39)(35,37)(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)(10,16)(12,22)(13,23)(14,24)(15,25)(17,30)(18,31)(19,21)(20,32)(26,40)(27,37)(28,38)(29,39)(33,35)(34,36);(9,12,14,28)(10,17,19,33)(11,22,24,38)(13,27,15,29)(16,30,21,35)(18,26,20,34)(23,37,25,39)(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, 55079);