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C₂×#27800 #6457580

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

Aliases

Subgroups

2370 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)(9,11)(10,12)(13,14)(15,16,20,22)(17,23,27,30)(18,28,26,21)(19,29,25,24);(3,5,6,4)(7,9,10,13)(8,11,12,14)(15,17,25,18,20,27,19,26)(16,21,29,30,22,28,24,23);(4,5)(8,12)(11,14)(16,22)(21,28)(23,30)(24,29);(15,18,25,27,20,26,19,17)(16,23,29,21,22,30,24,28)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6364776);