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C₂×#59278 #7666372

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

Aliases

Subgroups

6710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573568);