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C₂×#54149 #8102881

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

Aliases

Subgroups

7364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8010077);