Finite Group Databasebeta

?

← Prev (#7640961) Next (#7640963) →

C₂×#42505 #7640962

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

Aliases

Subgroups

6388 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)(19,20,22,24)(21,25,26,23);(3,4)(5,9)(6,7)(8,10)(12,13)(16,17)(19,21,22,26)(20,23,24,25);(4,7)(8,9)(11,13,15,12)(14,17,18,16)(19,21)(20,23)(22,26)(24,25);(3,4)(5,8)(6,7)(9,10)(11,14)(12,16)(13,17)(15,18)(19,20)(21,23)(22,24)(25,26);(3,5,6,10)(4,8,7,9)

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, 7548158);