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C₂×#23493 #6431879

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

Aliases

Subgroups

5534 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)(12,17)(13,19)(16,22)(20,21);(3,4)(5,6)(10,19)(12,21)(13,18)(17,20);(3,5,6,4)(7,9)(8,12)(10,20)(11,16)(13,22)(14,21)(15,18)(17,19);(9,16)(12,21)(15,22)(17,20)

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, 6339075);