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C₄×#1946 #354668

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

Aliases

Subgroups

1146 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)(9,10,13,18,14,19,23,17)(11,15,12,21,20,16,22,24);(6,8)(9,11,13,12,14,20,23,22)(10,15,18,21,19,16,17,24);(9,12,13,20,14,22,23,11)(10,16,17,21,19,15,18,24)

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, 261864);