Finite Group Databasebeta

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C₇₉×#62034 #34173723

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1768 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)(11,15,21,30)(12,22,25,31)(13,26,27,17)(16,23,32,24)(19,33,35,39)(20,37,38,29)(28,34,40,36)(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)(9,11,14,21)(10,15,18,30)(12,19,25,35)(13,20,27,38)(16,28,32,40)(17,29,26,37)(22,33,31,39)(23,34,24,36);(9,12)(10,16)(11,19)(13,23)(14,25)(15,28)(17,31)(18,32)(20,34)(21,35)(22,26)(24,27)(29,39)(30,40)(33,37)(36,38);(2,5)(6,8)(9,13,14,27)(10,17,18,26)(11,20,21,38)(12,23,25,24)(15,29,30,37)(16,31,32,22)(19,34,35,36)(28,39,40,33);(1,3,4,7)(2,6,5,8)(11,21)(15,30)(19,35)(20,38)(28,40)(29,37)(33,39)(34,36)

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, 55022);