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C₂×#21783 #6374202

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

Aliases

Subgroups

4240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6281398);