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C₂×#13532 #499536

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

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, 406732);