Finite Group Databasebeta

?

← Prev (#34173545) Next (#34173547) →

C₇₉×#61857 #34173546

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 111 points:

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

Conjugacy classes & character table

3871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 54845);