Finite Group Databasebeta

?

← Prev (#515154) Next (#515156) →

C₂×#14323 #515155

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

Aliases

Subgroups

4606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 422351);