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C₂²×#3284 #10576031

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

Aliases

Subgroups

11030 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)(9,10,15,12)(11,19,22,24)(13,18,14,17)(16,23,20,21);(9,11,15,22)(10,16,12,20)(13,21,14,23)(17,19,18,24);(6,8)(9,12,15,10)(11,20,22,16)(13,18,14,17)(19,21,24,23);(9,13)(10,17)(12,18)(14,15)(19,24)(21,23)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483227);