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C₂×C₄×#560 #7625932

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

Aliases

Subgroups

9318 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)(9,16)(10,15)(11,13)(12,18)(14,20)(17,21)(19,22);(7,9)(8,12)(10,18)(11,19)(13,21)(14,22)(15,16)(17,20);(8,13)(9,17)(12,16)(14,15)(18,19)(21,22);(8,14)(9,18)(12,21)(13,15)(16,22)(17,19)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533128);