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C₂×C₄×#551 #7625394

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

Aliases

Subgroups

9918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,5,6);(7,8,10,14)(9,15,16,12)(11,13,18,20)(17,21,22,19);(7,9,11,17)(8,12,13,19)(10,16,18,22)(14,15,20,21);(8,13)(12,19)(14,20)(15,21);(9,16)(12,15)(17,22)(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, 7532590);