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C₂×#62903 #10586244

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

Aliases

Subgroups

32374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493440);