Finite Group Databasebeta

?

← Prev (#7623091) Next (#7623093) →

C₂×#33685 #7623092

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12,14,19)(13,22,23,17)(15,18,26,33)(16,29,27,21)(20,35,34,28)(24,36,39,30)(25,32,40,38)(31,41,37,42);(4,7)(8,10)(11,13,14,23)(12,17,19,22)(15,24,26,39)(16,25,27,40)(18,30,33,36)(20,31,34,37)(21,32,29,38)(28,41,35,42);(12,18)(15,28)(16,27)(17,30)(19,33)(20,21)(22,36)(24,41)(25,40)(26,35)(29,34)(31,32)(37,38)(39,42);(3,5,6,9)(4,8,7,10)(13,23)(17,22)(24,39)(25,40)(30,36)(31,37)(32,38)(41,42)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530288);