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C₂×#54812 #8103526

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

Aliases

Subgroups

5796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8010722);