Finite Group Databasebeta

← Group #100342

Character table — Group #100342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111111-1-1-1-1-1-11-1-1-1-1-111-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111111-1-1-1-1-1-11-1-1-1-1-111-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-111-11
χ1111111111111-1-1-1-1-1-11-1-1-1-1-111-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-111-11
χ1211111111111-1-1-1-1-1-11-1-1-1-1-111-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-11-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-11-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ1722222222222222-2-2-222-22-2-2-2-2222-2-2-222-2-2000000000000000000000000000000
χ1822222222222222-2-2-222-22-2-2-2-22-2-2-222-2-222000000000000000000000000000000
χ1922222222222-2-2-22222-22-222-2-2-222-2-2-2-2-222000000000000000000000000000000
χ2022222222222-2-2-22222-22-222-2-2-2-2-2-22222-2-2000000000000000000000000000000
χ2122222222-2-2-2222222-222-2-2-222-200-200000022-2-222-2-20000000000000000000000
χ2222222222-2-2-2222222-222-2-2-222-200-2000000-2-222-2-2220000000000000000000000
χ2322222222-2-2-2222-2-2-2-22-2-222-2-2-200200000000000000000000002i−2i2i−2i0000000000
χ2422222222-2-2-2222-2-2-2-22-2-222-2-2-20020000000000000000000000−2i2i−2i2i0000000000
χ2522222222-2-2-2-2-2-2222-2-222-2-2-2-2200200000000000000000000002-2-220000000000
χ2622222222-2-2-2-2-2-2222-2-222-2-2-2-220020000000000000000000000-222-20000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-20000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ29222-2-2-2-2222-20002-2-2-20202-20000002i−2i2i−2i000000000022−2−222−2−20000i2−i2i2−i2000000
χ30222-2-2-2-2222-20002-2-2-20202-20000002i−2i2i−2i0000000000−2−222−2−2220000−i2i2−i2i2000000
χ31222-2-2-2-2222-20002-2-2-20202-2000000−2i2i−2i2i000000000022−2−222−2−20000−i2i2−i2i2000000
χ32222-2-2-2-2222-20002-2-2-20202-2000000−2i2i−2i2i0000000000−2−222−2−2220000i2−i2i2−i2000000
χ33222-2-2-2-2222-2000-222-20-20-220000002i−2i−2i2i0000000000i2i2−i2−i2−i2−i2i2i20000−222−2000000
χ34222-2-2-2-2222-2000-222-20-20-220000002i−2i−2i2i0000000000−i2−i2i2i2i2i2−i2−i200002−2−22000000
χ35222-2-2-2-2222-2000-222-20-20-22000000−2i2i2i−2i0000000000i2i2−i2−i2−i2−i2i2i200002−2−22000000
χ36222-2-2-2-2222-2000-222-20-20-22000000−2i2i2i−2i0000000000−i2−i2i2i2i2i2−i2−i20000−222−2000000
χ372-2-2-2-222200022-222-20-2-20002-20000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000002−22−200
χ382-2-2-2-222200022-222-20-2-20002-20000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200000000−22−2200
χ392-2-2-2-222200022-222-20-2-20002-2000000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200000000−22−2200
χ402-2-2-2-222200022-222-20-2-20002-2000000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000002−22−200
χ412-2-2-2-2222000-2-22-2-220220002-20000000000002-200-222−22−2−22−22000000002−2−2200
χ422-2-2-2-2222000-2-22-2-220220002-20000000000002-200-22−22−222−22−200000000−222−200
χ432-2-2-2-2222000-2-22-2-220220002-2000000000000-22002-22−22−2−22−2200000000−222−200
χ442-2-2-2-2222000-2-22-2-220220002-2000000000000-22002-2−22−222−22−2000000002−2−2200
χ45444-4-4-4-44-4-440004-4-44040-44000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-44000-44440-404-4000000000000000000000000000000000000000000
χ4744-44-44-4-40004-440000-4000000000000000022−220022−22000000000000000000000000
χ4844-44-44-4-40004-440000-40000000000000000−222200−2222000000000000000000000000
χ4944-44-44-4-4000-44-40000400000000000000002i2−2i200−2i22i2000000000000000000000000
χ5044-44-44-4-4000-44-4000040000000000000000−2i22i2002i2−2i2000000000000000000000000
χ514-444-4-44-44-44000000-4000000004-40000000000000000000000000000000000000
χ524-444-4-44-44-44000000-400000000-440000000000000000000000000000000000000
χ534-444-4-44-4-44-400000040000000000000004i−4i000000000000000000000000000000
χ544-444-4-44-4-44-40000004000000000000000−4i4i000000000000000000000000000000
χ554-44-444-4-44-4-44-4-4000440-400004000000000000000000000000000000000000000
χ564-44-444-4-44-4-4-4440004-4040000-4000000000000000000000000000000000000000
χ574-44-444-4-4-4444-4-4000-44040000-4000000000000000000000000000000000000000
χ584-44-444-4-4-444-444000-4-40-400004000000000000000000000000000000000000000
χ594-4-444-4-440000004-4400-4000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ604-4-444-4-440000004-4400-400000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ614-4-444-4-44000000-44-4004000000000000000000000002-2-22-222-200000000000000
χ624-4-444-4-44000000-44-400400000000000000000000000-222-22-2-2200000000000000
χ634-4-4-4-444400044-4-4-440-44000-440000000000000000000000000000000000000000
χ644-4-4-4-4444000-4-4444-404-4000-440000000000000000000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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