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C₂×#29639 #6434662

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

Aliases

Subgroups

4436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6341858);