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C₂×#44022 #7668169

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

Aliases

Subgroups

9852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(9,13)(11,14)(15,16)(17,18)(19,20)(21,22);(3,4,5,6)(7,8)(9,14)(10,12)(11,13)(16,20)(18,21);(7,8,10,12)(9,11,13,14)(15,17)(16,21)(18,20)(19,22);(3,4)(5,6)(7,8)(9,11)(10,12)(13,14)(15,18,19,21)(16,17,20,22);(7,9)(8,11)(10,13)(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, 7575365);