Finite Group Databasebeta

?

← Prev (#7667543) Next (#7667545) →

C₂×#43419 #7667544

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

Aliases

Subgroups

8134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574740);