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C₄×#3546 #7626192

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

Aliases

Subgroups

7820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7533388);