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C₂×#59184 #7666902

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

Aliases

Subgroups

9778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574098);