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C₂×#37699 #7635113

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

Aliases

Subgroups

9000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542309);