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C₂×#1308 #8123

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

Aliases

Subgroups

263 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 1111);