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C₂²×#1866 #6371327

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

Aliases

Subgroups

4830 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)(9,10,14,17,15,12,13,18)(11,19,21,16,23,24,22,20);(6,8)(9,11,14,21,15,23,13,22)(10,16,17,24,12,20,18,19);(9,12)(10,15)(11,20)(13,17)(14,18)(16,23)(19,21)(22,24)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278523);