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C₆₁×#61412 #29564845

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

3538 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 54400);