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C₂×#26944 #6443528

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

Aliases

Subgroups

2906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350724);