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C₂×#12668 #493133

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

Aliases

Subgroups

740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400329);