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C₂×#41456 #7639934

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

Aliases

Subgroups

5682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547130);