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C₂×#11246 #358068

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

Aliases

Subgroups

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265264);