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C₂×#24468 #6437926

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

Aliases

Subgroups

5136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345122);