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C₂×C₄×#554 #7625399

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

Aliases

Subgroups

8974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532595);