Finite Group Databasebeta

?

← Prev (#7623036) Next (#7623038) →

C₂×#33647 #7623037

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

Aliases

Subgroups

1692 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)(13,17)(14,18)(15,28)(16,19)(20,25)(21,26)(22,29)(23,38)(24,30)(27,33)(31,35)(32,36)(34,39)(37,40)(41,42);(4,7)(8,10)(11,13,16,24)(12,17,19,30)(14,22,27,37)(15,23,26,36)(18,29,33,40)(20,31,34,41)(21,32,28,38)(25,35,39,42);(3,5,6,9)(4,8,7,10)(12,18)(14,25)(15,26)(17,29)(19,33)(20,21)(22,35)(23,36)(27,39)(28,34)(30,40)(31,32)(37,42)(38,41);(12,19)(17,30)(18,33)(20,34)(21,28)(29,40)(31,41)(32,38)

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, 7530233);