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C₂×#13168 #495023

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

Aliases

Subgroups

762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 402219);