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C₂×#24406 #6437992

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

Aliases

Subgroups

5526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345188);