Finite Group Databasebeta

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C₈₃×#61800 #35289624

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

3818 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 54788);