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C₂×#10813 #353517

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

Aliases

Subgroups

1926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260713);