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C₂×#20926 #6371405

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

Aliases

Subgroups

6490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6278601);