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C₆₇×#61642 #30740893

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 107 points:

(1,2)(3,7)(4,6)(5,8)(9,10,15,19)(11,16,21,30)(12,23,25,33)(13,18,14,27)(17,28,34,24)(20,35,36,40)(22,31,26,32)(29,37,39,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,5)(4,8)(6,7)(9,11,15,21)(10,16,19,30)(12,20,25,36)(13,26,14,22)(17,29,34,39)(18,32,27,31)(23,35,33,40)(24,38,28,37);(9,12)(10,17)(11,20)(13,24)(14,28)(15,25)(16,29)(18,33)(19,34)(21,36)(22,37)(23,27)(26,38)(30,39)(31,35)(32,40);(3,8)(5,7)(11,21)(16,30)(20,36)(22,26)(29,39)(31,32)(35,40)(37,38);(2,6)(5,7)(9,13,15,14)(10,18,19,27)(11,22,21,26)(12,24,25,28)(16,31,30,32)(17,33,34,23)(20,37,36,38)(29,35,39,40)

Conjugacy classes & character table

3484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 54630);