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C₂×#12087 #483833

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

Aliases

Subgroups

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 391029);