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C₂×#39658 #7637261

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

Aliases

Subgroups

5626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7544457);