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C₂×#37747 #7634990

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

Aliases

Subgroups

8642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

(1,2);(8,11)(12,14)(16,17)(18,25)(22,24)(26,30);(4,6)(8,11)(9,13)(15,16,20,17)(18,21,25,23)(19,24,27,22)(26,29,30,28);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,17,20,16)(18,23,25,21)(19,24,27,22)(26,29,30,28);(15,18)(16,21)(17,23)(19,26)(20,25)(22,28)(24,29)(27,30);(3,4)(5,6)(7,9,10,13)(8,12,11,14)(15,19,20,27)(16,22,17,24)(18,26,25,30)(21,28,23,29)

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, 7542186);