Finite Group Databasebeta

?

← Prev (#6448741) Next (#6448743) →

C₂×#24174 #6448742

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

Aliases

Subgroups

3456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6355938);