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C₂×#24287 #6442593

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

Aliases

Subgroups

4472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349789);