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C₂×#52210 #7633541

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

Aliases

Subgroups

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540737);