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C₂×#23407 #6431731

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

Aliases

Subgroups

7818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338927);