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C₂×#21916 #6374759

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

Aliases

Subgroups

2386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281955);