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C₆₇×#61613 #30740864

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2056 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)(12,24)(13,18)(14,27)(15,19)(17,25)(20,34)(21,30)(22,31)(23,37)(26,32)(28,33)(29,35)(36,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,5)(4,8)(6,7)(9,11)(10,16)(12,20)(13,21)(14,23)(15,22)(17,29)(18,30)(19,31)(24,34)(25,35)(26,36)(27,37)(28,38)(32,39)(33,40);(9,12)(10,17)(11,20)(13,25)(14,28)(15,26)(16,29)(18,32)(19,33)(21,35)(22,36)(23,38)(24,27)(30,39)(31,40)(34,37);(3,8)(5,7)(9,13,15,14)(10,18,19,27)(11,21,22,23)(12,25,26,28)(16,30,31,37)(17,32,33,24)(20,35,36,38)(29,39,40,34);(2,6)(5,7)(11,22)(16,31)(20,36)(21,23)(29,40)(30,37)(34,39)(35,38)

Conjugacy classes & character table

3283 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 54601);