Finite Group Databasebeta

?

← Prev (#35289982) Next (#35289984) →

C₈₃×#62159 #35289983

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1712 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)(17,18,21,27)(19,28,30,23)(20,25,22,26)(24,31,32,29)(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)(17,19)(18,23)(20,31)(21,30)(22,29)(24,25)(26,32)(27,28);(17,19)(18,24)(20,29)(21,30)(22,31)(23,25)(26,28)(27,32);(3,10)(6,9)(11,16)(14,15)(17,20,21,22)(18,25,27,26)(19,29,30,31)(23,32,28,24);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(17,20,21,22)(18,26,27,25)(19,29,30,31)(23,24,28,32)

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, 55147);