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C₂×#46318 #7703051

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

Aliases

Subgroups

6898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610247);