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C₂×#25388 #6444335

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

Aliases

Subgroups

3388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351531);