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C₂×#24268 #6442742

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

Aliases

Subgroups

4822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349938);