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C₂×#12659 #493107

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

Aliases

Subgroups

846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400303);