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C₂×#36358 #7630012

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

Aliases

Subgroups

5886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537208);