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C₂×#16688 #611360

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

Aliases

Subgroups

3430 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)(13,17)(14,15)(16,18)(19,20,22,25)(21,24,26,23);(11,13)(12,16)(14,17)(15,18)(19,21,22,26)(20,23,25,24);(7,8,9,10)(11,13)(12,17)(14,16)(15,18)(19,21)(20,24)(22,26)(23,25);(3,4)(5,6)(11,14,15,12)(13,17,18,16)(19,20)(21,23)(22,25)(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, 518556);