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C₂×#30657 #7501394

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

Aliases

Subgroups

2466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4)(5,6)(7,8,10,12)(9,11,13,14)(15,16,18,19)(17,20,22,21);(7,8)(9,11)(10,12)(13,14)(15,17,18,22)(16,20,19,21);(4,6)(7,9,10,13)(8,11,12,14)(16,19)(17,21)(20,22);(4,6)(8,12)(11,14)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7408590);