Finite Group Databasebeta

← Group #12090296

Character table — Group #12090296

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222224444444444444444444888888888888888888888888888161616162020202020203232323232323232404040404040404040404080
order1222444455101010101010488888820202020202020202020202088840404040404040404040404040404040404040404040404044442244442020202020202020244448888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ5111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-111-1-1-1-1-1
χ6111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111
χ7111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111-11-1-111-1-1-1
χ8111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-11-111-1-1111
χ911111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111-1-111-1-1-11-1-1-1111111-1
χ1011111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1111111-1-111-1-11-1111-1-1-1-1-1-11
χ1111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11111111-1-111-1-111-11-111-1-1-1-111-1
χ1211111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1-1111-11-1-11111-1-11
χ1311111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-11111-1-1-1-111-11-1-1111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-111-1-1-1-1111-111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11111-1-1-1-11111-1-1-11-11-1-1-111-1-11
χ1611111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-111-1-11111-1-11-11-1111-1-111-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522222000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-20000001−521+521−521+521−521+521−521+52000000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5222-2-2000000−1+52−1−52−1+52−1−521−521+521−521+52000000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2-2220000001−521+521−521+52−1+52−1−52−1+52−1−52000000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-22-2000000−1+52−1−521−521+52−1+52−1−521−521+52000000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-22-220000001−521+52−1+52−1−521−521+52−1+52−1−52000000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2221−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-22000000−1+52−1−521−521+521−521+52−1+52−1−52000000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2221−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-222-20000001−521+52−1+52−1−52−1+52−1−521−521+52000000000000
χ2522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000
χ2622222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-20000001+521−521+521−521+521−521+521−52000000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5222-2-2000000−1−52−1+52−1−52−1+521+521−521+521−52000000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-2-2220000001+521−521+521−52−1−52−1+52−1−52−1+52000000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-22-2000000−1−52−1+521+521−52−1−52−1+521+521−52000000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-22-220000001+521−52−1−52−1+521+521−52−1−52−1+52000000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2221+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2-22000000−1−52−1+521+521−521+521−52−1−52−1+52000000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2221+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-222-20000001+521−52−1−52−1+52−1−52−1+521+521−52000000000000
χ3322222-2-2222222222-20000222222-2-2-2-2-2-2-2-2-2000000000022-2-222-2-200000000000000222200000000000-2-20000000
χ3422222-2-2222222222-20000222222-2-2-2-2-2-2-2-2-2000000000022-2-222-2-200000000000000-2-2-2-200000000000220000000
χ3522222-2-2222222222-20000-2-22222-2-2-2-2-2-2-2-220000000000-2-222-2-2220000000000000022-2-200000000000-220000000
χ3622222-2-2222222222-20000-2-22222-2-2-2-2-2-2-2-220000000000-2-222-2-22200000000000000-2-222000000000002-20000000
χ372222-222-222222222-222-2-200-2-2-2-22222-2-2-2-200022-2-222-2-200000000000000000000220000000000002-2-2000000000
χ382222-222-222222222-222-2-200-2-2-2-22222-2-2-2-200022-2-222-2-200000000000000000000-2-2000000000000-222000000000
χ392222-222-222222222-2-2-22200-2-2-2-22222-2-2-2-2000-2-222-2-2220000000000000000000022000000000000-2-22000000000
χ402222-222-222222222-2-2-22200-2-2-2-22222-2-2-2-2000-2-222-2-22200000000000000000000-2-200000000000022-2000000000
χ412-2-22-20022222-2-2-2-202−22−22-22-22-20000000002−22−22−22−22−22-2002-20022−2−222−2−20000002i−2i2i−2i0000000000000i2−i2i2−i2000
χ422-2-22-20022222-2-2-2-202−22−22-22-22-20000000002−22−22−22−22−22-2002-20022−2−222−2−2000000−2i2i−2i2i0000000000000−i2i2−i2i2000
χ432-2-22-20022222-2-2-2-202−22−2-222-22-2000000000−222−22−22−22−2-2200-2200−2−222−2−2220000002i−2i−2i2i0000000000000i2−i2−i2i2000
χ442-2-22-20022222-2-2-2-202−22−2-222-22-2000000000−222−22−22−22−2-2200-2200−2−222−2−222000000−2i2i2i−2i0000000000000−i2i2i2−i2000
χ452-2-22-20022222-2-2-2-20−22−222-22-22-2000000000−22−22−22−22−222-2002-200−2−222−2−2220000002i−2i2i−2i0000000000000−i2i2−i2i2000
χ462-2-22-20022222-2-2-2-20−22−222-22-22-2000000000−22−22−22−22−222-2002-200−2−222−2−222000000−2i2i−2i2i0000000000000i2−i2i2−i2000
χ472-2-22-20022222-2-2-2-20−22−22-222-22-20000000002−2−22−22−22−22-2200-220022−2−222−2−20000002i−2i−2i2i0000000000000−i2i2i2−i2000
χ482-2-22-20022222-2-2-2-20−22−22-222-22-20000000002−2−22−22−22−22-2200-220022−2−222−2−2000000−2i2i2i−2i0000000000000i2−i2−i2i2000
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4000044−1+5−1+5−1−5−1−51−51−51+51+51−51−51+51+5-40000000000−1+5−1+51−51−5−1−5−1−51+51+500000000000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-40000-4-4−1+5−1+5−1−5−1−51−51−51+51+51−51−51+51+5400000000001−51−5−1+5−1+51+51+5−1−5−1−500000000000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4000044−1−5−1−5−1+5−1+51+51+51−51−51+51+51−51−5-40000000000−1−5−1−51+51+5−1+5−1+51−51−500000000000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-40000-4-4−1−5−1−5−1+5−1+51+51+51−51−51+51+51−51−5400000000001+51+5−1−5−1−51−51−5−1+5−1+500000000000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-444-4-4001−51−51+51+5−1+5−1+5−1−5−1−51−51−51+51+5000−1+5−1+51−51−5−1−5−1−51+51+50000000000000000000000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-444001−51−51+51+5−1+5−1+5−1−5−1−51−51−51+51+50001−51−5−1+5−1+51+51+5−1−5−1−50000000000000000000000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-444-4-4001+51+51−51−5−1−5−1−5−1+5−1+51+51+51−51−5000−1−5−1−51+51+5−1+5−1+51−51−50000000000000000000000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-444001+51+51−51−5−1−5−1−5−1+5−1+51+51+51−51−50001+51+5−1−5−1−51−51−5−1+5−1+50000000000000000000000000000000000000000000000
χ574444-4-4-4-4444444444000000-4-4-4-4-4-4-4-44444000000000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−540000001−51−51+51+51−51−51+51+5−1+5−1+5−1−5−1−500000000000000000002ζ12−2ζ28−2ζ12+2ζ282ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000
χ594444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−540000001−51−51+51+51−51−51+51+5−1+5−1+5−1−5−1−50000000000000000000−2ζ12+2ζ282ζ12−2ζ28−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000
χ604444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+540000001+51+51−51−51+51+51−51−5−1−5−1−5−1+5−1+50000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000
χ614444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+540000001+51+51−51−51+51+51−51−5−1−5−1−5−1+5−1+500000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000
χ6244-4-404-4044-4-444-4-4000000000004-44-4000000000000000000000000000000000004-4000000000000000000000000
χ6344-4-404-4044-4-444-4-4000000000004-44-400000000000000000000000000000000000-44000000000000000000000000
χ6444-4-40-44044-4-444-4-400000000000-44-44000000000000000000000000000000000000000000000000000000000022−220
χ6544-4-40-44044-4-444-4-400000000000-44-440000000000000000000000000000000000000000000000000000000000−22220
χ664-4-44400-44444-4-4-4-4022−22−222200-44-440000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ674-4-44400-44444-4-4-4-40−222222−2200-44-4400000000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ684-4-44400-4−1+5−1−5−1+5−1−51−51+51−51+5022−22−2222001−5−1+51+5−1−500000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39002ζ12−2ζ28−2ζ12+2ζ2800−2ζ4+2ζ362ζ4−2ζ36−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000000000000000
χ694-4-44400-4−1+5−1−5−1+5−1−51−51+51−51+5022−22−2222001−5−1+51+5−1−500000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900−2ζ12+2ζ282ζ12−2ζ28002ζ4−2ζ36−2ζ4+2ζ36ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000000000000000
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χ928-88-80000−2−25−2+252+252−252+252−25−2−25−2+250000000000000004ζ4−4ζ36−4ζ4+4ζ364ζ12−4ζ28−4ζ12+4ζ28000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.