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C₂×#40390 #7637482

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

Aliases

Subgroups

7144 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)(19,20,23,24)(21,25,26,22);(3,4,6,8)(5,7,10,9)(12,16)(14,17)(21,26)(22,25);(11,12)(13,17)(14,18)(15,16)(19,21)(20,22)(23,26)(24,25);(3,5)(4,7)(6,10)(8,9)(11,13,15,18)(12,17,16,14);(3,4)(5,7)(6,8)(9,10)(11,14,15,17)(12,18,16,13)(19,22)(20,21)(23,25)(24,26)

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, 7544678);