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C₅₉×#62034 #28474143

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 99 points:

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

Conjugacy classes & character table

2891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 55022);