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C₂×#12031 #483419

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

Aliases

Subgroups

454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 50 points:

(1,2);(3,4,6,9,7,10,13,16)(5,8,12,15,11,14,17,18)(19,20)(21,30,33,45)(22,27)(23,36)(24,39)(25,29)(26,32,41,48)(28,37)(31,44,34,46)(35,43)(38,50)(40,47,42,49);(3,5)(4,8)(6,12)(7,11)(9,15)(10,14)(13,17)(16,18)(19,21,23,32,24,31,37,47,25,33,38,48,22,34,35,49)(20,26,28,30,27,42,36,46,29,41,43,45,39,40,50,44);(5,11)(8,14)(12,17)(15,18)(19,22,25,24)(20,27,29,39)(21,31,33,34)(23,35,38,37)(26,40,41,42)(28,36,43,50)(30,44,45,46)(32,47,48,49)

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, 390615);