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C₂×#20655 #6370802

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

Aliases

Subgroups

4878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6277998);