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C₂×#19997 #6358389

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

Aliases

Subgroups

1704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265585);