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C₂×#51791 #7707723

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

Aliases

Subgroups

5446 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)(13,17)(14,15)(16,18)(19,20,22,24)(21,25,26,23);(3,5)(4,8)(6,9)(7,10)(12,15)(16,17);(3,5,7,10)(4,9,6,8)(11,13)(12,16)(14,18)(15,17)(19,21,22,26)(20,23,24,25);(3,5)(4,9)(6,8)(7,10)(11,12)(13,16)(14,15)(17,18);(3,6,7,4)(5,8,10,9)(11,13)(12,16)(14,18)(15,17)

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, 7614919);