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C₂×#12658 #493104

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

Aliases

Subgroups

854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 400300);