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C₂×#21038 #6371594

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

Aliases

Subgroups

2662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278790);