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C₂×#30243 #6433768

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

Aliases

Subgroups

3528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6340964);