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C₂×#14789 #607726

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

Aliases

Subgroups

5194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 514922);