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C₂×#8709 #189762

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

Aliases

Subgroups

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 96958);