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C₂²×#2308 #7625261

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

Aliases

Subgroups

39170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532457);