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C₂×#42999 #7667139

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

Aliases

Subgroups

9922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574335);