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C₂×#37374 #7634771

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

Aliases

Subgroups

9174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541967);