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C₂×#37317 #7634660

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

Aliases

Subgroups

6898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541856);