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C₄×#1951 #354683

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

Aliases

Subgroups

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261879);