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C₂×#23830 #6432638

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

Aliases

Subgroups

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339834);