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C₂×#3407 #62623

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

Aliases

Subgroups

1037 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55611);