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C₂×#11183 #357937

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

Aliases

Subgroups

3146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265133);