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C₂×#12065 #483586

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

Aliases

Subgroups

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390782);