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C₂×#16564 #611134

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

Aliases

Subgroups

4306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518330);