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C₂×#59568 #7665909

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

Aliases

Subgroups

9960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573105);