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C₂×#12077 #483798

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

Aliases

Subgroups

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390994);