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C₂×#36244 #7629892

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

Aliases

Subgroups

8622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537088);