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C₂×#29263 #6463596

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

Aliases

Subgroups

2290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6370792);