Finite Group Databasebeta

?

← Prev (#7509806) Next (#7509808) →

C₂×#32466 #7509807

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

Aliases

Subgroups

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7417003);