Finite Group Databasebeta

?

← Prev (#29565480) Next (#29565482) →

C₆₁×#62048 #29565481

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1796 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)(12,25,27,34)(13,20,15,18)(17,29,32,26)(22,36,38,40)(23,31,28,33)(30,39,35,37)(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)(13,28)(14,24)(15,23)(17,30)(18,33)(19,21)(20,31)(25,40)(26,39)(27,38)(29,37)(32,35)(34,36);(9,12)(10,17)(11,22)(13,26)(14,27)(15,29)(16,30)(18,25)(19,32)(20,34)(21,35)(23,37)(24,38)(28,39)(31,36)(33,40);(2,5)(6,8)(9,13,14,15)(10,18,19,20)(11,23,24,28)(12,26,27,29)(16,31,21,33)(17,25,32,34)(22,37,38,39)(30,36,35,40);(1,3,4,7)(2,6,5,8)(10,19)(11,24)(17,32)(18,20)(22,38)(23,28)(25,34)(37,39)

Conjugacy classes & character table

2989 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 55036);