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C₇₉×#62080 #34173769

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1778 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)(11,15,21,31)(12,23,26,33)(13,27,28,17)(16,24,34,25)(19,35,37,40)(20,32,22,30)(29,38,39,36)(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)(12,19)(13,22)(14,21)(16,29)(17,32)(18,31)(20,28)(23,35)(24,38)(25,36)(26,37)(27,30)(33,40)(34,39);(9,12)(10,16)(11,19)(13,24)(14,26)(15,29)(17,33)(18,34)(20,36)(21,37)(22,38)(23,27)(25,28)(30,35)(31,39)(32,40);(2,5)(6,8)(9,13,14,28)(10,17,18,27)(11,20,21,22)(12,24,26,25)(15,30,31,32)(16,33,34,23)(19,36,37,38)(29,35,39,40);(1,3,4,7)(2,6,5,8)(11,21)(15,31)(19,37)(20,22)(29,39)(30,32)(35,40)(36,38)

Conjugacy classes & character table

3634 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 55068);