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C₂×#59155 #7666118

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

Aliases

Subgroups

8122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573314);