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C₂×#45074 #7669490

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

Aliases

Subgroups

6632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576686);