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C₄×#1815 #354960

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

Aliases

Subgroups

1564 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)(9,10,14,17,15,12,13,23)(11,18,21,19,22,24,20,16);(9,11,13,20,15,22,14,21)(10,16,17,18,12,19,23,24);(6,8)(9,12)(10,15)(11,19)(13,23)(14,17)(16,22)(18,21)(20,24)

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, 262156);