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C₄×#576 #60171

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

Aliases

Subgroups

1413 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53159);