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C₂×#13492 #499370

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

Aliases

Subgroups

860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

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

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, 406566);