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C₂²×#1436 #513342

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

Aliases

Subgroups

13674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420538);