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C₂×#53128 #8092859

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

Aliases

Subgroups

6598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 8000055);