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C₈₃×#61473 #35289297

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 123 points:

(2,5)(6,8)(9,10,14,18)(11,15,20,29)(12,22,24,32)(13,25,27,17)(16,26,31,23)(19,33,34,40)(21,37,36,30)(28,38,39,35)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,2)(3,6)(4,5)(7,8)(9,11)(10,15)(12,19)(13,21)(14,20)(16,28)(17,30)(18,29)(22,33)(23,35)(24,34)(25,37)(26,38)(27,36)(31,39)(32,40);(9,12,14,24)(10,16,18,31)(11,19,20,34)(13,26,27,23)(15,28,29,39)(17,32,25,22)(21,38,36,35)(30,40,37,33);(2,5)(6,8);(1,3,4,7)(2,6,5,8)(11,20)(15,29)(19,34)(21,36)(28,39)(30,37)(33,40)(35,38)

Conjugacy classes & character table

4814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 54461);