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C₂×#16569 #611140

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

Aliases

Subgroups

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518336);