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C₂×#3563 #62733

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

Aliases

Subgroups

3229 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55721);