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C₂×#3566 #62742

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

Aliases

Subgroups

3347 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)(21,24)(22,27)(23,28)(25,29)(26,31)(30,32)(33,34);(4,8)(9,14)(10,15)(16,18)(20,21)(22,29)(26,28)(30,34);(3,4)(5,9)(6,10)(7,8)(11,14)(12,16)(13,15)(17,18)(19,21,24,20)(22,27,29,25)(23,28,31,26)(30,33,34,32);(3,5)(4,9)(6,12)(7,11)(8,14)(10,16)(13,17)(15,18)(19,22)(20,25)(21,27)(23,30)(24,29)(26,32)(28,33)(31,34);(3,6,7,13)(4,10,8,15)(5,12,11,17)(9,16,14,18)(19,23,24,31)(20,26,21,28)(22,30,29,34)(25,32,27,33)

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, 55730);