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C₂×#35584 #7628968

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

Aliases

Subgroups

10642 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)(17,21)(19,22);(3,4,5,6)(7,9,11,10)(8,12,13,14)(15,16,18,20)(17,19,21,22);(9,10)(12,14)(15,17,18,21)(16,19,20,22);(7,10,11,9)(8,12,13,14);(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, 7536164);