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C₂×#45999 #7702663

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

Aliases

Subgroups

8794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7609859);