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C₂×#13533 #499538

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

Aliases

Subgroups

864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406734);