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C₂×#23177 #6382729

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

Aliases

Subgroups

3416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289925);