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C₂×#16449 #610963

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

Aliases

Subgroups

3786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518159);