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C₂×#10816 #353523

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

Aliases

Subgroups

2054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260719);