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C₂×#14566 #521027

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

Aliases

Subgroups

5330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 428223);