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C₂×#16273 #610752

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

Aliases

Subgroups

5690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 517948);