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C₂×#20460 #6369926

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

Aliases

Subgroups

3050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 6277122);