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C₂×#51609 #7707485

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

Aliases

Subgroups

5698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614681);