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C₂×#1840 #20771

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

Aliases

Subgroups

447 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13759);