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C₂×#62246 #10577527

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

Aliases

Subgroups

6778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12,15,18)(13,19,22,26)(14,23,20,17)(16,24,25,21);(3,5)(4,7)(6,10)(8,9);(11,13,20,24,15,22,14,21)(12,16,23,26,18,25,17,19);(5,10)(7,9);(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, 10484723);