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C₂×#10772 #353351

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

Aliases

Subgroups

4462 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)(9,17,19,21)(10,13)(11,15)(12,16)(14,18,22,20);(4,6)(8,13,16,15)(14,17,22,21);(7,9)(8,14)(10,18)(11,20)(12,19)(13,17)(15,21)(16,22)

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, 260547);