Finite Group Databasebeta

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C₈₃×#61491 #35289315

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

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, 54479);