Finite Group Databasebeta

?

← Prev (#7666126) Next (#7666128) →

C₂×#59265 #7666127

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

Aliases

Subgroups

7038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573323);