Finite Group Databasebeta

?

← Prev (#10586365) Next (#10586367) →

C₂×#63041 #10586366

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

Aliases

Subgroups

35756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

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, 10493562);