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C₂²×#2930 #10574188

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

Aliases

Subgroups

11178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481384);