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C₂×#59025 #7665964

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

Aliases

Subgroups

9164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573160);