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C₈₃×#62173 #35289997

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 115 points:

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

Conjugacy classes & character table

4067 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 55161);