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C₇₉×#62060 #34173749

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

4108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 55048);