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C₂²×#2344 #7625331

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

Aliases

Subgroups

13690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532527);