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C₂×#52666 #8092105

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

Aliases

Subgroups

6374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7999301);