Finite Group Databasebeta

?

← Prev (#6433717) Next (#6433719) →

C₂×#30188 #6433718

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

Aliases

Subgroups

2444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6340914);