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C₂×#35465 #7628834

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

Aliases

Subgroups

8602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7536030);