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C₂×#19910 #6358279

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

Aliases

Subgroups

1936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265475);