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C₂×#20113 #6359444

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

Aliases

Subgroups

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266640);