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C₂²×#1884 #6371442

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

Aliases

Subgroups

6482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278638);