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C₂×#40785 #7638849

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

Aliases

Subgroups

7224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546045);