Finite Group Databasebeta

?

← Prev (#7667178) Next (#7667180) →

C₂×#43068 #7667179

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

Aliases

Subgroups

5972 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574375);