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C₂×#36493 #7630179

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

Aliases

Subgroups

9906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537375);