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C₄×#1782 #354794

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

Aliases

Subgroups

4162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4);(5,6)(7,8)(9,10)(11,17,19,14)(12,15)(13,16)(18,23,24,21)(20,22);(9,11)(10,14)(12,18)(13,19)(15,21)(16,17)(20,24)(22,23);(6,8)(9,12,13,20)(10,15,16,22)(11,18,19,24)(14,21,17,23)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261990);