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C₂×#1373 #12010

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

Aliases

Subgroups

115 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 4998);