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C₂×#2009 #23411

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

Aliases

Subgroups

963 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 16399);