Finite Group Databasebeta

?

← Prev (#7638027) Next (#7638029) →

C₂×#40174 #7638028

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

Aliases

Subgroups

6314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545224);