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C₂×#14539 #520996

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

Aliases

Subgroups

5854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 428192);