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C₂×#21906 #6374736

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

Aliases

Subgroups

3442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6281932);