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C₂×#11304 #358339

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

Aliases

Subgroups

1610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265535);