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C₂×#25810 #6443283

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

Aliases

Subgroups

5156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350479);