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C₄×#3041 #6372814

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

Aliases

Subgroups

3074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 6280010);