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C₂×#34918 #7628085

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

Aliases

Subgroups

6738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535281);