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C₂×#13040 #494564

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

Aliases

Subgroups

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401760);