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C₂×#3555 #62751

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

Aliases

Subgroups

3223 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55739);