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C₂×#25802 #6443274

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

Aliases

Subgroups

5080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350470);