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C₂×#24223 #6442553

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

Aliases

Subgroups

4760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6349749);