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C₂×#45616 #7701944

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

Aliases

Subgroups

6356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609140);