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C₂×#27669 #6457154

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

Aliases

Subgroups

2456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6364350);