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C₂×#51056 #7707156

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

Aliases

Subgroups

6936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,9)(6,7)(8,10)(11,12)(13,18)(14,17)(15,16)(19,20,24,26)(21,25,22,23);(4,7)(8,9)(11,13,16,14)(12,17,15,18)(19,21)(20,25)(22,24)(23,26);(13,14)(17,18)(20,26)(21,22);(3,4)(5,8)(6,7)(9,10)(11,14,16,13)(12,17,15,18)(19,22,24,21)(20,23,26,25);(3,5,6,10)(4,8,7,9)(11,15,16,12)(13,17,14,18)(19,23)(20,21)(22,26)(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, 7614352);