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C₂×#12646 #493073

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

Aliases

Subgroups

1152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400269);