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C₂×#59312 #7666501

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

Aliases

Subgroups

8014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573697);