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C₄×#552 #34163

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

Aliases

Subgroups

1188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27151);