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C₂×#31283 #7504289

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

Aliases

Subgroups

2282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411485);