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C₂×#53410 #8100265

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

Aliases

Subgroups

5764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8007461);