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C₂×#44228 #7668174

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

Aliases

Subgroups

10928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7575370);