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C₂×#12000 #483321

• 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)(12,16,17,22)(13,19)(14,21)(18,25,24,23)(20,26);(11,12,13,16,14,18,19,23,15,17,20,22,21,24,26,25);(12,17)(16,22)(18,24)(23,25)

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, 390517);