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C₇₉×#62090 #34173779

• 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)(11,19,22,15)(12,23,25,31)(13,27,28,17)(16,24,32,26)(20,35,37,40)(21,30,39,34)(29,38,33,36)(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)(9,11,14,22)(10,15,18,19)(12,20,25,37)(13,21,28,39)(16,29,32,33)(17,30,27,34)(23,40,31,35)(24,36,26,38);(9,12)(10,16)(11,20)(13,24)(14,25)(15,29)(17,31)(18,32)(19,33)(21,36)(22,37)(23,27)(26,28)(30,35)(34,40)(38,39);(2,5)(6,8)(9,13,14,28)(10,17,18,27)(11,21,22,39)(12,24,25,26)(15,30,19,34)(16,31,32,23)(20,36,37,38)(29,35,33,40);(1,3,4,7)(2,6,5,8)(10,18)(11,22)(16,32)(17,27)(20,37)(21,39)(23,31)(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, 55078);