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C₂×#12651 #493087

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

Aliases

Subgroups

1114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400283);