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C₂×#2606 #34862

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

Aliases

Subgroups

983 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27850);