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C₂×#16044 #609998

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

Aliases

Subgroups

4594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 517194);