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C₂×#37686 #7635004

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

Aliases

Subgroups

8502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542200);