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C₂×#12009 #483335

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

Aliases

Subgroups

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390531);