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C₂×#499 #3158

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

Aliases

Subgroups

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1890);