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C₂×#42134 #7640337

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

Aliases

Subgroups

5440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547533);