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C₂×#12618 #492983

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

Aliases

Subgroups

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400179);