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C₂×#61038 #10576051

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

Aliases

Subgroups

10792 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)(9,16)(10,14)(11,20)(12,15)(13,19)(17,18)(21,22);(7,9)(8,13)(10,19)(11,21)(12,17)(14,18)(15,22)(16,20);(4,6)(9,17)(13,22)(16,18)(19,21);(7,8)(9,18)(10,14)(11,20)(12,15)(13,21)(16,17)(19,22);(7,10,12,11)(8,14,15,20)(9,19,17,21)(13,18,22,16)

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, 10483247);