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C₄×#3542 #7626166

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

Aliases

Subgroups

7914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7533362);