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C₂×#13578 #512591

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

Aliases

Subgroups

1164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419787);