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C₂×#10957 #354044

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

Aliases

Subgroups

3150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261240);