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C₂×#13334 #498870

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

Aliases

Subgroups

1624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406066);