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C₄×#3481 #7625406

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

Aliases

Subgroups

9144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7532602);