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C₂×#31284 #7504288

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

Aliases

Subgroups

2314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7411484);