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C₂×#20431 #6369883

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

Aliases

Subgroups

3498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,5,6)(7,8,10,9)(11,12)(13,16)(14,18)(15,17)(19,23)(20,22)(21,24)(25,26);(4,6)(11,13,14,19,15,20,21,25)(12,16,18,23,17,22,24,26);(7,9,10,8)(11,12)(13,16)(14,18)(15,17)(19,23)(20,22)(21,24)(25,26);(12,17)(16,22)(18,24)(23,26)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277079);