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C₂²×#1978 #6372024

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

Aliases

Subgroups

6058 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279220);