Finite Group Databasebeta

?

← Prev (#7637796) Next (#7637798) →

C₂×#39929 #7637797

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

Aliases

Subgroups

6096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544993);