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C₂×#13472 #499317

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

Aliases

Subgroups

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406513);