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C₂×#16697 #611427

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

Aliases

Subgroups

4342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518623);