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C₂×#45041 #7669441

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

Aliases

Subgroups

7478 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)(13,18)(14,17)(15,16)(19,20)(21,25)(22,23)(24,26);(3,4)(5,10)(6,7)(8,9)(11,13)(12,17)(14,16)(15,18)(20,23)(21,26);(4,7)(8,10)(13,14)(17,18)(19,20,22,23)(21,24,26,25);(3,4)(5,8)(6,7)(9,10)(11,14,16,13)(12,17,15,18)(19,20)(21,24)(22,23)(25,26);(3,5,6,9)(4,8,7,10)(11,15,16,12)(13,17,14,18)(19,21,22,26)(20,24,23,25)

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, 7576637);