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C₂×#1454 #17322

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

Aliases

Subgroups

401 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 10310);