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C₂×#18755 #6348668

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

Aliases

Subgroups

3230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255864);