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C₄×#2435 #514833

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

Aliases

Subgroups

7530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422029);