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C₂×#13287 #495383

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

Aliases

Subgroups

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402579);