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C₂×#51691 #7707457

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

Aliases

Subgroups

6446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614653);