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C₄×#3490 #7625641

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

Aliases

Subgroups

9490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3,4);(5,6)(7,13)(8,12)(9,11)(10,14)(15,19)(16,18)(17,20);(5,7,9,15)(6,10,11,17)(8,14,16,20)(12,13,18,19);(6,11)(10,17)(12,18)(13,19);(7,14)(10,13)(15,20)(17,19);(6,12)(10,13)(11,18)(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, 7532837);