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C₂×#51165 #7707110

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

Aliases

Subgroups

7118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614306);