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C₂×#12678 #493161

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

Aliases

Subgroups

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400357);