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C₂×C₄×#543 #7625313

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

Aliases

Subgroups

9466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532509);