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C₄×#2190 #495696

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

Aliases

Subgroups

1129 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402892);