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C₂×#20705 #6370889

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

Aliases

Subgroups

5146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278085);