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C₂×#11127 #357810

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

Aliases

Subgroups

3270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265006);