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C₂×#10805 #353498

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

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, 260694);