Finite Group Databasebeta

← Group #12009792

Character table — Group #12009792

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size111122222222222244444444444444444444444444444888888888888888888888816161616161616161616161616161616161616164040404040404040404040408080
order1222224455101010101010224444444101010102020202020202020202020202020202044101010102020202020202020202020202020202088884040404040404040404040404040404044444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−i1111iiii−i−i−i−i-1-1
χ61111111111111111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1−i−i−i−iiiii11
χ71111111111111111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii1111−i−i−i−iiiii-1-1
χ81111111111111111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1iiii−i−i−i−i11
χ9111111-1-11111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ10111111-1-11111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ11111111-1-11111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1111-1
χ12111111-1-11111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-11
χ13111111-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii-11
χ14111111-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i1-1
χ15111111-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i-11
χ16111111-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii1-1
χ172222222222222222222-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000
χ182222222222222222-2-22-2-2-2-22222222222222222222222-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000
χ1922222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222222222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−522222−1+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+52−1−52−1−5200000000000000
χ2022222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222222222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000000
χ2122222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-2-222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000000000000
χ2222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-2-222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000000000000
χ2322222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-21−521−521+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+522i2i−2i−2i−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ700000000000000
χ2422222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-21−521−521+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+52−2i−2i2i2iζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700000000000000
χ2522222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ1800000000000000
χ2622222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ1800000000000000
χ2722222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222222222−1−52−1−52−1+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+5222−1−52−1−52−1+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+522222−1−52−1−52−1+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+5200000000000000
χ2822222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222222222−1−52−1−52−1+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+5222−1−52−1−52−1+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+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000
χ2922222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-2-222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000000000000
χ3022222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-2-222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000000000000
χ3122222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-2222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-21+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+521−521−522i2i−2i−2i−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900000000000000
χ3222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-2222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-21+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+521−521−52−2i−2i2i2iζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900000000000000
χ3322222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ1400000000000000
χ3422222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ1400000000000000
χ35222222-2-22222222222-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000
χ36222222-2-222222222-2-2-22222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000
χ37222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-222-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-22−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000000000000
χ38222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-222-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-22−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000000000000
χ39222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-2-2-2-2-222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2−1+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+522-22-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000
χ40222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-2-2-2-2-222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2−1+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+52-22-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000
χ41222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2-2222222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+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+520000ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ1800000000000000
χ42222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2-2222222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+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+520000−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ1800000000000000
χ43222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2-2-2-222-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522i−2i−2i2i−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700000000000000
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χ9688-8-80000−2−25−2+252+252+25−2−252−252−25−2+250000000000000004ζ3−4ζ7−4ζ3+4ζ7004ζ11−4ζ19−4ζ11+4ζ190000000000000000000000000000000000000000000000000000000000000000
χ9788-8-80000−2−25−2+252+252+25−2−252−252−25−2+25000000000000000−4ζ3+4ζ74ζ3−4ζ700−4ζ11+4ζ194ζ11−4ζ190000000000000000000000000000000000000000000000000000000000000000
χ988-8-88008i−8i−2+25−2−252−25−2+252−252+25−2−252+250000000000000−4ζ11−4ζ194ζ11+4ζ1900−4ζ3−4ζ74ζ3+4ζ7000000000000000000000000000000000000000000000000000000000000000000
χ998-8-88008i−8i−2−25−2+252+25−2−252+252−25−2+252−250000000000000−4ζ3−4ζ74ζ3+4ζ700−4ζ11−4ζ194ζ11+4ζ19000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8800−8i8i−2+25−2−252−25−2+252−252+25−2−252+2500000000000004ζ11+4ζ19−4ζ11−4ζ19004ζ3+4ζ7−4ζ3−4ζ7000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800−8i8i−2−25−2+252+25−2−252+252−25−2+252−2500000000000004ζ3+4ζ7−4ζ3−4ζ7004ζ11+4ζ19−4ζ11−4ζ19000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.