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C₆₇×#61655 #30740906

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2032 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)(11,16)(12,23)(13,19)(14,27)(15,18)(17,24)(20,35)(21,32)(22,30)(25,34)(26,31)(28,33)(29,38)(36,40)(37,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,5)(4,8)(6,7)(9,11,15,21)(10,16,18,32)(12,20,25,36)(13,26,14,22)(17,29,33,39)(19,31,27,30)(23,35,34,40)(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)(30,35)(31,40)(32,39);(3,8)(5,7)(10,18)(11,21)(17,33)(19,27)(20,36)(22,26)(23,34)(37,38);(2,6)(5,7)(9,13,15,14)(10,19,18,27)(11,22,21,26)(12,24,25,28)(16,30,32,31)(17,34,33,23)(20,37,36,38)(29,35,39,40)

Conjugacy classes & character table

3082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 54643);