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C₇₉×#62061 #34173750

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(2,5)(3,7)(9,10)(11,15)(12,24)(13,17)(14,19)(16,26)(18,28)(20,35)(21,30)(22,31)(23,33)(25,32)(27,34)(29,36)(37,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(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);(9,12,14,27)(10,16,19,32)(11,20,22,37)(13,25,28,26)(15,29,31,40)(17,24,18,34)(21,36,23,38)(30,39,33,35);(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, 55049);