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C₂×#59357 #7665764

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

Aliases

Subgroups

7166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7572960);