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C₂×#19774 #6358114

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

Aliases

Subgroups

1867 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265310);