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C₂×#34578 #7627733

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

Aliases

Subgroups

6970 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)(11,12,14,16)(13,17,18,15)(19,20)(21,23)(22,24)(25,26);(4,7)(8,10)(19,21)(20,23)(22,25)(24,26);(11,13,14,18)(12,15,16,17)(21,25)(23,26);(20,24)(23,26);(3,5,6,9)(4,8,7,10)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7534929);