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C₂×C₄×#559 #7625401

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

Aliases

Subgroups

9126 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)(16,19)(20,21);(8,10)(12,13)(15,16,18,19)(17,21,22,20);(7,9,11,14)(8,12,10,13);(7,10,11,8)(9,13,14,12)(15,17,18,22)(16,20,19,21)

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, 7532597);