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C₂×#12737 #493525

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

Aliases

Subgroups

3210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400721);