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C₂×#16319 #610802

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

Aliases

Subgroups

5842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 517998);