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C₂×#13497 #499383

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

Aliases

Subgroups

676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406579);