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C₄×#575 #60158

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

Aliases

Subgroups

1421 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53146);