Finite Group Databasebeta

?

← Prev (#8099018) Next (#8099020) →

C₂×#56346 #8099019

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

Aliases

Subgroups

9316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006215);