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C₂×#16882 #611662

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

Aliases

Subgroups

4530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518858);