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C₂×#9529 #202061

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

Aliases

Subgroups

1286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 109257);