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C₄×#2204 #495762

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

Aliases

Subgroups

1196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402958);