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C₂×#54847 #8102216

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

Aliases

Subgroups

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009412);