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C₂×#12030 #483418

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

Aliases

Subgroups

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,6,9,7,10,13,16)(5,8,12,15,11,14,17,18)(20,24,25,30)(21,27)(22,29)(26,33,32,31)(28,34);(3,5)(4,8)(6,12)(7,11)(9,15)(10,14)(13,17)(16,18)(19,20,21,24,22,26,27,31,23,25,28,30,29,32,34,33);(5,11)(8,14)(12,17)(15,18)(20,25)(24,30)(26,32)(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, 390614);