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C₂×#11068 #357736

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

Aliases

Subgroups

2914 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)(11,12,15,19,16,14,24,18)(13,17,22,20,23,25,21,26);(3,4,5,6)(11,13)(12,17)(14,25)(15,22)(16,23)(18,26)(19,20)(21,24);(8,10)(11,14)(12,16)(13,20)(15,18)(17,21)(19,24)(22,25)(23,26)

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, 264932);