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C₂×#20900 #6371360

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

Aliases

Subgroups

6662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278556);