Finite Group Databasebeta

?

← Prev (#7670055) Next (#7670057) →

C₂×#45418 #7670056

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

Aliases

Subgroups

11226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7577252);