Finite Group Databasebeta

?

← Prev (#7630218) Next (#7630220) →

C₂×#36530 #7630219

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

Aliases

Subgroups

8066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537415);