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C₂×#13376 #498978

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

Aliases

Subgroups

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406174);