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C₂×#45508 #7701940

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

Aliases

Subgroups

6844 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609136);