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C₂²×#1507 #6343289

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

Aliases

Subgroups

6958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250485);