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C₂×#42096 #7640352

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

Aliases

Subgroups

6700 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)(19,20,23,22)(21,25,26,24);(3,4)(5,9)(6,7)(8,10)(11,12)(13,14)(15,16)(17,18)(20,22)(24,25);(4,7)(8,9)(12,16)(13,17)(19,21,23,26)(20,24,22,25);(3,4)(5,8)(6,7)(9,10)(11,13,15,17)(12,14,16,18)(19,21)(20,24)(22,25)(23,26);(3,5,6,10)(4,8,7,9)(11,14)(12,17)(13,16)(15,18)(19,22,23,20)(21,25,26,24)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7547548);