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C₂×#12670 #493138

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

Aliases

Subgroups

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400334);