Finite Group Databasebeta

?

← Prev (#6441909) Next (#6441911) →

C₂×#26422 #6441910

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

Aliases

Subgroups

2510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349106);