Finite Group Databasebeta

← Group #258421

Character table — Group #258421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422224444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11-1-111-1-1-1-111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111111
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-11111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1111111-111-1-1-1-1
χ91111111111-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1
χ101111111111-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ111111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ121111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1
χ131111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-111-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1111-1-111
χ141111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-11-1-111-1-1
χ151111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-111111-1-1-1-111-11111-1-1
χ161111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-111-111-1-1-1-111111111-1-1-1-11-1-11111-1-1-1-1-111
χ1722222222222222-2-222-2-2-2-2-2220000-200220000-2220000000000000000-2000000-2000000
χ1822222222222222-2-222-2-2-2-2-2220000-200-2-20000-2-2-2000000000000000020000002000000
χ192222222222-2-2-2-2-2-222-2-2-222-2-20000-2002200002-2-200000000000000002000000-2000000
χ202222222222-2-2-2-2-2-222-2-2-222-2-20000-200-2-200002220000000000000000-20000002000000
χ2122222222-2-2222222-2-222-222-2-22222-2-2-200-2-222-200000000000000000000000000000000
χ2222222222-2-2222222-2-222-222-2-2-2-2-2-2-2220022-2-2-200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-22-2-2-2-20000200000000200000000000000000002-2002-20000000
χ2422222222-2-22222-2-2-2-2-2-22-2-2-2-2000020000000020000000000000000000-2200-220000000
χ2522222222-2-2-2-2-2-222-2-222-2-2-2222222-22200-2-2-2-2200000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-2-222-2-2-2-2-2-2-2002222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222220000200000000-200000000000000000002-200-220000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222220000200000000-20000000000000000000-22002-20000000
χ29222-2-2-2-222200002-2-2-22-2-200002i2i−2i−2i200002i−2i0000022-2-20000000000000002i−2i000000000
χ30222-2-2-2-222200002-2-2-22-2-200002i2i−2i−2i200002i−2i00000-2-222000000000000000−2i2i000000000
χ31222-2-2-2-222200002-2-2-22-2-20000−2i−2i2i2i20000−2i2i0000022-2-2000000000000000−2i2i000000000
χ32222-2-2-2-222200002-2-2-22-2-20000−2i−2i2i2i20000−2i2i00000-2-2220000000000000002i−2i000000000
χ33222-2-2-2-22-2-200002-2222-2200002i2i−2i−2i-20000−2i2i0000000002i2i−2i−2i00000000000000002-20000
χ34222-2-2-2-22-2-200002-2222-2200002i2i−2i−2i-20000−2i2i000000000−2i−2i2i2i0000000000000000-220000
χ35222-2-2-2-22-2-200002-2222-220000−2i−2i2i2i-200002i−2i0000000002i2i−2i−2i0000000000000000-220000
χ36222-2-2-2-22-2-200002-2222-220000−2i−2i2i2i-200002i−2i000000000−2i−2i2i2i00000000000000002-20000
χ372-22-222-2-22-22i2i−2i−2i002-2000002i−2i00000002-2000002i−2ii2−i2i2−i22−22−2i2i2−i2−i222−2−200000000000000
χ382-22-222-2-22-22i2i−2i−2i002-2000002i−2i00000002-2000002i−2i−i2i2−i2i2−22−22−i2−i2i2i2−2−22200000000000000
χ392-22-222-2-22-22i2i−2i−2i002-2000002i−2i0000000-2200000−2i2ii2−i2i2−i22−22−2−i2−i2i2i2−2−22200000000000000
χ402-22-222-2-22-22i2i−2i−2i002-2000002i−2i0000000-2200000−2i2i−i2i2−i2i2−22−22i2i2−i2−i222−2−200000000000000
χ412-22-222-2-22-2−2i−2i2i2i002-200000−2i2i00000002-200000−2i2ii2−i2i2−i2−22−22i2i2−i2−i2−2−22200000000000000
χ422-22-222-2-22-2−2i−2i2i2i002-200000−2i2i00000002-200000−2i2i−i2i2−i2i22−22−2−i2−i2i2i222−2−200000000000000
χ432-22-222-2-22-2−2i−2i2i2i002-200000−2i2i0000000-22000002i−2ii2−i2i2−i2−22−22−i2−i2i2i222−2−200000000000000
χ442-22-222-2-22-2−2i−2i2i2i002-200000−2i2i0000000-22000002i−2i−i2i2−i2i22−22−2i2i2−i2−i2−2−22200000000000000
χ452-2-222-2-22002-22-22200-2-202-2002i−2i2i−2i00000002i−2i00000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-2-222-2-22002-22-22200-2-202-2002i−2i2i−2i00000002i−2i00000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-2-222-2-22002-22-22200-2-202-200−2i2i−2i2i0000000−2i2i00000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-2-222-2-22002-22-22200-2-202-200−2i2i−2i2i0000000−2i2i00000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-2-222-2-2200-22-222200-2-20-22002i−2i2i−2i0000000−2i2i00000000000i2−i2i2−i2−i2i2−i2i200000000002−2−22
χ502-2-222-2-2200-22-222200-2-20-22002i−2i2i−2i0000000−2i2i00000000000−i2i2−i2i2i2−i2i2−i20000000000−222−2
χ512-2-222-2-2200-22-222200-2-20-2200−2i2i−2i2i00000002i−2i00000000000i2−i2i2−i2−i2i2−i2i20000000000−222−2
χ522-2-222-2-2200-22-222200-2-20-2200−2i2i−2i2i00000002i−2i00000000000−i2i2−i2i2i2−i2i2−i200000000002−2−22
χ53444-4-4-4-44440000-44-4-4-44400000000-400000000000000000000000000000000000000000
χ54444-4-4-4-44-4-40000-4444-44-400000000400000000000000000000000000000000000000000
χ5544-4-44-44-4004i−4i−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ5644-4-44-44-4004i−4i−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ5744-4-44-44-400−4i4i4i−4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ5844-4-44-44-400−4i4i4i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ594-444-4-44-44-4000000-44000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ604-444-4-44-44-4000000-4400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ614-444-4-44-4-440000004-40000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ624-444-4-44-4-440000004-4000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ634-44-444-4-4-444i4i−4i−4i00-4400000−4i4i0000000000000000000000000000000000000000000000
χ644-44-444-4-4-44−4i−4i4i4i00-44000004i−4i0000000000000000000000000000000000000000000000
χ654-4-444-4-44004-44-4-4-400440-44000000000000000000000000000000000000000000000000
χ664-4-444-4-4400-44-44-4-4004404-4000000000000000000000000000000000000000000000000
χ674-4-4-4-44440000004-400-44000004-4-44000000000000000000000000000000000000000000
χ684-4-4-4-44440000004-400-4400000-444-4000000000000000000000000000000000000000000
χ694-4-4-4-4444000000-44004-400000000004-4000000000000000000000000000000000000000
χ704-4-4-4-4444000000-44004-40000000000-44000000000000000000000000000000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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