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C₂²×#2051 #6431938

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

Aliases

Subgroups

5262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339134);