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C₂×#20338 #6369739

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

Aliases

Subgroups

7582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276935);