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C₂×#12579 #492893

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

Aliases

Subgroups

2322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400089);