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C₂×#2082 #23651

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

Aliases

Subgroups

439 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

46 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 16639);