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C₂×#35772 #7629413

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

Aliases

Subgroups

8936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536609);