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C₇₉×#62048 #34173737

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 119 points:

(2,5)(3,7)(9,10,14,18)(11,19,22,15)(12,24,26,33)(13,28,29,17)(16,25,34,27)(20,36,38,40)(21,31,23,32)(30,37,35,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(1,2)(3,6)(4,5)(7,8)(9,11)(10,15)(12,20)(13,23)(14,22)(16,30)(17,32)(18,19)(21,29)(24,40)(25,39)(26,38)(27,37)(28,31)(33,36)(34,35);(9,12)(10,16)(11,20)(13,25)(14,26)(15,30)(17,33)(18,34)(19,35)(21,37)(22,38)(23,39)(24,28)(27,29)(31,40)(32,36);(2,5)(6,8)(9,13,14,29)(10,17,18,28)(11,21,22,23)(12,25,26,27)(15,31,19,32)(16,33,34,24)(20,37,38,39)(30,40,35,36);(1,3,4,7)(2,6,5,8)(10,18)(11,22)(16,34)(17,28)(20,38)(21,23)(24,33)(37,39)

Conjugacy classes & character table

3871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 55036);