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C₂×#12628 #493005

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

Aliases

Subgroups

1746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400201);