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C₂×#2833 #36668

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

Aliases

Subgroups

859 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 29656);