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C₂²×#2165 #7622558

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

Aliases

Subgroups

1658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529754);