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C₂×#12047 #483510

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

Aliases

Subgroups

486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390706);