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C₂×#52048 #7708098

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

Aliases

Subgroups

6084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615294);