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C₂²×#2364 #7625367

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

Aliases

Subgroups

16826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7532563);