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C₂×#41877 #7640200

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

Aliases

Subgroups

6224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7547396);