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C₂×#13474 #499320

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

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, 406516);