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C₂×#17330 #6342452

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

Aliases

Subgroups

2110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6249648);