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C₂×#59735 #7666753

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

Aliases

Subgroups

8468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,5)(7,8,12,11)(9,10,14,13)(16,19)(17,21);(3,4,6,5)(9,14)(10,13)(15,16,18,19)(17,20,21,22);(7,9,12,14)(8,13,11,10)(15,16)(17,20)(18,19)(21,22);(7,10)(8,9)(11,14)(12,13)(15,17)(16,20)(18,21)(19,22);(3,5,6,4)(7,11,12,8)(9,10,14,13)(15,17)(16,20)(18,21)(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, 7573949);