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C₂×#13523 #499516

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

Aliases

Subgroups

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406712);