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C₂×#21536 #6372863

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

Aliases

Subgroups

3214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(7,8,10,9)(12,16)(14,17)(18,23)(19,24)(20,26)(22,25);(11,12,17,24,15,19,14,16)(13,20,25,23,21,18,22,26);(4,6)(11,13)(12,18)(14,22)(15,21)(16,23)(17,25)(19,20)(24,26);(7,9,10,8)(13,21)(18,20)(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, 6280059);