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C₂×#11656 #481310

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

Aliases

Subgroups

780 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)(21,30,33,46)(22,26)(23,37)(24,29)(25,32,41,50)(27,35)(28,36)(31,44,34,47)(38,40,48,42)(39,43)(45,49);(3,5)(4,8)(6,12)(7,11)(9,15)(10,14)(13,17)(16,18)(19,21)(20,25)(22,34)(23,38)(24,33)(26,42)(27,44)(28,40)(29,41)(30,43)(31,36)(32,49)(35,50)(37,46)(39,48)(45,47);(5,11)(8,14)(12,17)(15,18)(19,22,24,36)(20,26,29,28)(21,31,33,34)(23,35,39,49)(25,40,41,42)(27,43,45,37)(30,44,46,47)(32,48,50,38)

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, 388506);