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C₂×#14304 #515123

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

Aliases

Subgroups

4874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422319);