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C₂×#40729 #7638909

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

Aliases

Subgroups

6288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546105);