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C₂²×#2183 #7622639

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

Aliases

Subgroups

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

(1,2);(3,4);(5,6)(7,12)(8,10)(9,11)(13,14,16,20,17,15,22,23,18,21,25,28,26,24,19,27);(5,7,9,8)(6,10,11,12);(5,8,9,7)(6,10,11,12)(13,15,16,23,17,21,22,28,18,24,25,27,26,14,19,20)

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529835);