Finite Group Databasebeta

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C₈₃×#61797 #35289621

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1802 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)(19,26)(21,23)(25,28)(27,32)(29,31)(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)(19,27)(20,23)(21,30)(22,24)(25,29)(26,28)(31,32);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,19,22,29)(18,25,24,27)(20,28,30,32)(21,26,23,31);(3,11)(6,9)(10,16)(13,15)(17,20)(18,21)(19,28)(22,30)(23,24)(25,26)(27,31)(29,32);(2,8)(6,9)(7,14)(13,15)(17,21,22,23)(18,20,24,30)(19,26,29,31)(25,28,27,32)

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, 54785);