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C₂×#12666 #493128

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

Aliases

Subgroups

764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400324);