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C₅₃×#61676 #27269188

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 93 points:

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

Conjugacy classes & character table

2438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 54664);