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C₂×#12983 #494419

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

Aliases

Subgroups

1432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,11,16,12,15,25,28,13,17,26,31,10,24,19,34)(9,18,21,32,22,30,35,37,23,33,36,38,20,14,27,29);(7,9,19,27,10,20,26,36,13,23,25,35,12,22,11,21)(8,14,28,32,24,33,16,29,17,30,34,38,15,18,31,37);(4,6)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401615);