Finite Group Databasebeta

← Group #290992

Character table — Group #290992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444224444444444488888888888888888888888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ511111111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ811111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ91111111111111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-111-1
χ101111111111111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-11-11
χ111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-111-1
χ121111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-11-11
χ131111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11-1-11
χ141111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-11-11-1
χ151111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-11
χ161111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-11-1
χ172222222222-2-2-2222222-2-2-222-2-222-222000000000000000000000000000000000000-2-200
χ182222222222-2-2-2222222-2-2-222-2-2-2-2-2-2-20000000000000000000000000000000000002200
χ192222222222-2-2-2-2-2-2-222-222-2-2-2-2222-2-20000000000000000000000000000000000002-200
χ202222222222-2-2-2-2-2-2-222-222-2-2-2-2-2-2222000000000000000000000000000000000000-2200
χ2122222222-2-22222222-2-2222-2-2-2-200-20022220000000000000000000000000000-2-2000000
χ2222222222-2-22222222-2-2222-2-2-2-200-200-2-2-2-2000000000000000000000000000022000000
χ2322222222-2-2222-2-2-2-2-2-22-2-222-2-20020022-2-20000000000000000000000000000-22000000
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-200200-2-22200000000000000000000000000002-2000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22200200000022-2-2000000000000000000000000002-20000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-222002000000-2-22200000000000000000000000000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-200000022-2-200000000000000000000000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000-2-222000000000000000000000000002-20000
χ29222-2-2-2-22222-2-20000-2-2200002-20000000002i−2i2i−2i2i2i−2i−2i0000000022-2-20000000000000000
χ30222-2-2-2-22222-2-20000-2-2200002-20000000002i−2i2i−2i−2i−2i2i2i00000000-2-2220000000000000000
χ31222-2-2-2-22222-2-20000-2-2200002-2000000000−2i2i−2i2i2i2i−2i−2i00000000-2-2220000000000000000
χ32222-2-2-2-22222-2-20000-2-2200002-2000000000−2i2i−2i2i−2i−2i2i2i0000000022-2-20000000000000000
χ33222-2-2-2-22-2-2-222000022-200002-20000000002i−2i−2i2i000022-2-22i2i−2i−2i00000000000000000000
χ34222-2-2-2-22-2-2-222000022-200002-20000000002i−2i−2i2i0000-2-222−2i−2i2i2i00000000000000000000
χ35222-2-2-2-22-2-2-222000022-200002-2000000000−2i2i2i−2i000022-2-2−2i−2i2i2i00000000000000000000
χ36222-2-2-2-22-2-2-222000022-200002-2000000000−2i2i2i−2i0000-2-2222i2i−2i−2i00000000000000000000
χ372-222-22-2-22-20002i2i−2i−2i2-20002i−2i002-202i−2i00000000000000002−22−2i2−i2i2−i222−2−2i2i2−i2−i200000000
χ382-222-22-2-22-20002i2i−2i−2i2-20002i−2i002-202i−2i0000000000000000−22−22−i2i2−i2i2−2−222−i2−i2i2i200000000
χ392-222-22-2-22-20002i2i−2i−2i2-20002i−2i00-220−2i2i00000000000000002−22−2i2−i2i2−i2−2−222−i2−i2i2i200000000
χ402-222-22-2-22-20002i2i−2i−2i2-20002i−2i00-220−2i2i0000000000000000−22−22−i2i2−i2i222−2−2i2i2−i2−i200000000
χ412-222-22-2-22-2000−2i−2i2i2i2-2000−2i2i002-20−2i2i00000000000000002−22−2−i2i2−i2i222−2−2−i2−i2i2i200000000
χ422-222-22-2-22-2000−2i−2i2i2i2-2000−2i2i002-20−2i2i0000000000000000−22−22i2−i2i2−i2−2−222i2i2−i2−i200000000
χ432-222-22-2-22-2000−2i−2i2i2i2-2000−2i2i00-2202i−2i00000000000000002−22−2−i2i2−i2i2−2−222i2i2−i2−i200000000
χ442-222-22-2-22-2000−2i−2i2i2i2-2000−2i2i00-2202i−2i0000000000000000−22−22i2−i2i2−i222−2−2−i2−i2i2i200000000
χ452-2-2-222-220022-22-22-200-22-20000000002i−2i2i−2i00002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i200000000
χ462-2-2-222-220022-22-22-200-22-20000000002i−2i2i−2i0000−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i200000000
χ472-2-2-222-220022-22-22-200-22-2000000000−2i2i−2i2i00002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i200000000
χ482-2-2-222-220022-22-22-200-22-2000000000−2i2i−2i2i0000−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i200000000
χ492-2-2-222-220022-2-22-2200-2-220000000002i−2i−2i2i00002−22−2−22−2200000000i2−i2i2−i2−i2i2−i2i200000000
χ502-2-2-222-220022-2-22-2200-2-220000000002i−2i−2i2i0000−22−222−22−200000000−i2i2−i2i2i2−i2i2−i200000000
χ512-2-2-222-220022-2-22-2200-2-22000000000−2i2i2i−2i00002−22−2−22−2200000000−i2i2−i2i2i2−i2i2−i200000000
χ522-2-2-222-220022-2-22-2200-2-22000000000−2i2i2i−2i0000−22−222−22−200000000i2−i2i2−i2−i2i2−i2i200000000
χ53444-4-4-4-4444-4440000-4-4-40000-44000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-44-4-400004440000-44000000000000000000000000000000000000000000000
χ5544-4-4-444-4000004i−4i−4i4i000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ5644-4-4-444-4000004i−4i−4i4i00000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ5744-4-4-444-400000−4i4i4i−4i000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ5844-4-4-444-400000−4i4i4i−4i00000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ594-444-44-4-4-440004i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ604-444-44-4-4-44000−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ614-44-44-44-44-40000000-44000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ624-44-44-44-44-40000000-4400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-44-44-44-4-4400000004-400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ644-44-44-44-4-4400000004-40000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ654-4-44-4-444004-44000000-400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ664-4-44-4-444004-44000000-40000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ674-4-44-4-44400-44-400000040000000000000000000000022−22−2222000000000000000000000000
χ684-4-44-4-44400-44-4000000400000000000000000000000−222222−22000000000000000000000000
χ694-4-4-444-4400-4-444-44-4004-440000000000000000000000000000000000000000000000000
χ704-4-4-444-4400-4-44-44-440044-40000000000000000000000000000000000000000000000000
χ7188-888-8-8-8000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).