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C₂×#16543 #611097

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

Aliases

Subgroups

4090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518293);