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C₂×#35780 #7629222

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

Aliases

Subgroups

6718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536418);