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C₂×#12064 #483580

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

Aliases

Subgroups

546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390776);