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C₂×#20839 #6371256

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

Aliases

Subgroups

4986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278452);