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C₂×#37186 #7634572

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

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, 7541768);