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C₂×#12665 #493122

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

Aliases

Subgroups

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400318);