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C₂×#13476 #499321

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

Aliases

Subgroups

968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406517);