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C₂×#43174 #7667315

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

Aliases

Subgroups

7322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574511);