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C₂×#20744 #6370973

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

Aliases

Subgroups

5002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278169);