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C₂×#1953 #21183

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

Aliases

Subgroups

429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14171);