Finite Group Databasebeta

← Group #12090491

Character table — Group #12090491

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222224444444444444444444888888888888888888888888888161616162020202020203232323232323232404040404040404040404080
order1222444455101010101010488888820202020202020202020202088840404040404040404040404040404040404040404040404044444444442020202020202020222448888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1
χ5111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-111-1-111-1-1-1
χ6111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-1111
χ7111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111-1111-1-1-1-111-1
χ8111111111111111111111-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-11-1-1-11111-1-11
χ911111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1
χ1011111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-11111-1-1-1-1-1-1-11
χ1111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1-1-11111-111-1111-1-1-1-1-1
χ1211111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-111111
χ1311111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-11111-1-1-1-111-1-11-11-1-111-1-11
χ1411111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-111-1-1-1-11111-11-111-1-111-1
χ1511111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111111-1-1-1-11111-1-1-11-1-11-1-1-1-1111
χ1611111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1-1-111-1-11111-1-11-111-11111-1-1-1
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+52−1−521−521+52−1+52−1−521−521+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+52−1+52−1−521−521+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+522-2-22000000−1+52−1−52−1+52−1−521−521+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+52-222-20000001−521+521−521+52−1+52−1−52−1+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+52−1−52−1−52−1−52−1−522-22-2000000−1+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+52−1−52−1−52−1−52−1−52-22-220000001−521+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+521+521−52−1−52−1+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+521−52−1−52−1+521+521−52−1−52−1+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+521−521−521−521−522-2-22000000−1−52−1+52−1−52−1+521+521−521+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+521−521−521−521−52-222-20000001+521−521+521−52−1−52−1+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+522-22-2000000−1−52−1+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+52-22-220000001+521−52−1−52−1+52−1−52−1+521+521−52000000000000
χ33222222-2-222222222-2000022-2-2-2-2-2-2-2-22222-2000000000022-2-222-2-2000000000000002222000000000-2-2000000000
χ34222222-2-222222222-2000022-2-2-2-2-2-2-2-22222-2000000000022-2-222-2-200000000000000-2-2-2-200000000022000000000
χ35222222-2-222222222-20000-2-2-2-2-2-2-2-2-2-2222220000000000-2-222-2-2220000000000000022-2-2000000000-22000000000
χ36222222-2-222222222-20000-2-2-2-2-2-2-2-2-2-2222220000000000-2-222-2-22200000000000000-2-2220000000002-2000000000
χ372222-2-22222222222-222-2-20022-2-222-2-2-2-2-2-200022-2-222-2-20000000000000000000022000000000000200-2-20000000
χ382222-2-22222222222-222-2-20022-2-222-2-2-2-2-2-200022-2-222-2-200000000000000000000-2-2000000000000-200220000000
χ392222-2-22222222222-2-2-2220022-2-222-2-2-2-2-2-2000-2-222-2-2220000000000000000000022000000000000-2002-20000000
χ402222-2-22222222222-2-2-2220022-2-222-2-2-2-2-2-2000-2-222-2-22200000000000000000000-2-2000000000000200-220000000
χ412-22-22-20022-2-2-2-2220i2−i2i2−i22-2000000002-22-20i2−i2i2−i2i2−i2i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i20000002i−2i2i−2i0000000000000002−22−20
χ422-22-22-20022-2-2-2-2220i2−i2i2−i22-2000000002-22-20i2−i2i2−i2i2−i2i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2i2i000000000000000−22−220
χ432-22-22-20022-2-2-2-2220i2−i2i2−i2-22000000002-22-20−i2i2i2−i2i2−i2i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i20000002i−2i−2i2i0000000000000002−2−220
χ442-22-22-20022-2-2-2-2220i2−i2i2−i2-22000000002-22-20−i2i2i2−i2i2−i2i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i2000000−2i2i2i−2i000000000000000−222−20
χ452-22-22-20022-2-2-2-2220−i2i2−i2i22-2000000002-22-20−i2i2−i2i2−i2i2−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i20000002i−2i2i−2i000000000000000−22−220
χ462-22-22-20022-2-2-2-2220−i2i2−i2i22-2000000002-22-20−i2i2−i2i2−i2i2−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i2000000−2i2i−2i2i0000000000000002−22−20
χ472-22-22-20022-2-2-2-2220−i2i2−i2i2-22000000002-22-20i2−i2−i2i2−i2i2−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i20000002i−2i−2i2i000000000000000−222−20
χ482-22-22-20022-2-2-2-2220−i2i2−i2i2-22000000002-22-20i2−i2−i2i2−i2i2−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i2000000−2i2i2i−2i0000000000000002−2−220
χ49444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-40000441−51−51−51−51+51+51+51+5−1+5−1+5−1−5−1−5-40000000000−1+5−1+51−51−5−1−5−1−51+51+500000000000000000000000000000000000000
χ50444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-40000-4-41−51−51−51−51+51+51+51+5−1+5−1+5−1−5−1−5400000000001−51−5−1+5−1+51+51+5−1−5−1−500000000000000000000000000000000000000
χ51444444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-40000441+51+51+51+51−51−51−51−5−1−5−1−5−1+5−1+5-40000000000−1−5−1−51+51+5−1+5−1+51−51−500000000000000000000000000000000000000
χ52444444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-40000-4-41+51+51+51+51−51−51−51−5−1−5−1−5−1+5−1+5400000000001+51+5−1−5−1−51−51−5−1+5−1+500000000000000000000000000000000000000
χ534444-4-444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-444-4-400−1+5−1+51−51−5−1−5−1−51+51+51−51−51+51+5000−1+5−1+51−51−5−1−5−1−51+51+50000000000000000000000000000000000000000000000
χ544444-4-444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-4-44400−1+5−1+51−51−5−1−5−1−51+51+51−51−51+51+50001−51−5−1+5−1+51+51+5−1−5−1−50000000000000000000000000000000000000000000000
χ554444-4-444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-444-4-400−1−5−1−51+51+5−1+5−1+51−51−51+51+51−51−5000−1−5−1−51+51+5−1+5−1+51−51−50000000000000000000000000000000000000000000000
χ564444-4-444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-4-44400−1−5−1−51+51+5−1+5−1+51−51−51+51+51−51−50001+51+5−1−5−1−51−51−5−1+5−1+50000000000000000000000000000000000000000000000
χ574444-4-4-4-4444444444000000-4-444-4-444-4-4-4-4000000000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−540000001−51−5−1+5−1+51+51+5−1−5−1−51−51−51+51+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+5−1−540000001−51−5−1+5−1+51+51+5−1−5−1−51−51−51+51+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+5−1−5−1−51−51−5−1+5−1+51+51+51−51−50000000000000000000−2ζ4+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+5−1−5−1−51−51−5−1+5−1+51+51+51−51−500000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000
χ624-44-44-400−1+5−1−51−51−51+51+5−1+5−1−502i2−2i22i2−2i24-400000000−1+51−5−1−51+502i2−2i2ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−1+51−500−1−51+500ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39000000000000000000000000000000
χ634-44-44-400−1+5−1−51−51−51+51+5−1+5−1−502i2−2i22i2−2i2-4400000000−1+51−5−1−51+50−2i22i2ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ391−5−1+5001+5−1−500−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39000000000000000000000000000000
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χ804-4-44004-4444-44-4-4-400000004-4004-4000000000000000000000000000000000000000000000000000000002i2−2i200000
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χ898-8-88008-8−2+25−2−25−2+252−25−2−252+252−252+250000000−2+252−2500−2−252+25000000000000000000000000000000000000000000000000000000000000000
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χ928-8-8800-88−2−25−2+25−2−252+25−2+252−252+252−2500000002+25−2−25002−25−2+25000000000000000000000000000000000000000000000000000000000000000

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