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C₂×#27344 #6449443

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

Aliases

Subgroups

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6356639);