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C₂×#12078 #483800

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

Aliases

Subgroups

544 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)(11,12,14,19,15,20,25,17)(13,21,24,18,23,16,22,26);(12,16)(13,22)(14,25)(17,26)(18,19)(20,21)(23,24);(3,5,6,8,7,9,10,4)(12,17,20,19)(13,23)(16,26,21,18)(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, 390996);