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C₂×#24224 #6442552

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

Aliases

Subgroups

4944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,5)(7,8)(9,15)(10,18)(11,14)(12,16)(13,19)(17,22)(20,21);(3,4,6,5)(10,19)(12,21)(13,18)(16,20);(7,9,11,17)(8,12,14,21)(10,20,19,16)(13,22,18,15);(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, 6349748);