Finite Group Databasebeta

?

← Prev (#6373521) Next (#6373523) →

C₂×#21661 #6373522

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

Aliases

Subgroups

2086 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)(11,12,17,22,18,23,16,34)(13,24,28,36,29,40,27,19)(14,30,15,21,33,38,32,20)(25,37,41,42,31,35,26,39);(4,7)(8,10)(11,13,16,27,18,29,17,28)(12,19,22,24,23,36,34,40)(14,31,32,41,33,25,15,26)(20,37,30,42,21,35,38,39);(3,5,6,9)(4,8,7,10)(11,14,16,32,18,33,17,15)(12,20,22,30,23,21,34,38)(13,25,27,26,29,31,28,41)(19,35,24,39,36,37,40,42);(11,15,17,33,18,32,16,14)(12,21,22,38,23,20,34,30)(13,26,28,25,29,41,27,31)(19,35,24,39,36,37,40,42)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280718);