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C₄×#2198 #495743

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

Aliases

Subgroups

1248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402939);