Finite Group Databasebeta

?

← Prev (#7665914) Next (#7665916) →

C₂×#59529 #7665915

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

Aliases

Subgroups

6320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573111);