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C₂×#39422 #7636624

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

Aliases

Subgroups

8178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543820);