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C₂×#41084 #7639411

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

Aliases

Subgroups

5714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546607);