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C₂×#3568 #62736

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

Aliases

Subgroups

3363 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55724);