Finite Group Databasebeta

?

← Prev (#34173735) Next (#34173737) →

C₇₉×#62047 #34173736

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 103 points:

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

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, 55035);