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C₂×#3240 #60853

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

Aliases

Subgroups

895 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53841);