Finite Group Databasebeta

← Group #13020530

Character table — Group #13020530

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111224444444444448888888888888881010161616161616161616202020202040404040404040404040408080808080
order12222222445101010101010104441010101020202020202020202242020202020202020222444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ4111111111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iii
χ5111111111111111111-1-111111-1-1-1-1-1-1-1-111-11111-1-1-1-1111111-1-111111111-1-1-1-1-1
χ6111111111111111111-1-111111-1-1-1-1-1-1-1-111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ911111111-1-11111111111-111111111111111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-111-1-1-11-11-1
χ1011111111-1-11111111111-111111111111111-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-111-1-11-11
χ1111111111-1-11111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1ii−i−i−i−iii1i−i−ii
χ1211111111-1-11111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1−i−iiiii−i−i1−iii−i
χ1311111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-111-1-111-1-11-11-11
χ1411111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-111-1-11111-11-1
χ1511111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-111111ii−i−i−i−iii-1−iii−i
χ1611111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-111111−i−iiiii−i−i-1i−i−ii
χ17222222-2-2222222222200-2-2-2-2-20000000022022-2-200002-2-222-2000000000000000
χ18222222-2-2222222222200-2-2-2-2-200000000-2-2022-2-20000-222-2-22000000000000000
χ19222222-2-2-2-222222222002-2-2-2-200000000220-2-22200002-2-2-2-22000000000000000
χ20222222-2-2-2-222222222002-2-2-2-200000000-2-20-2-2220000-22222-2000000000000000
χ212222-2-22-2002-2-222-2-2200022-2-20000000022000000000-22-200000002-2002-200000
χ222222-2-22-2002-2-222-2-2200022-2-20000000022000000000-22-20000000-2200-2200000
χ232222-2-22-2002-2-222-2-2200022-2-200000000-2-20000000002-2200000002i−2i00−2i2i00000
χ242222-2-22-2002-2-222-2-2200022-2-200000000-2-20000000002-220000000−2i2i002i−2i00000
χ252222-2-2-22002-2-222-2-22000-2-2220000000022000000000-2-22000002-2002-20000000
χ262222-2-2-22002-2-222-2-22000-2-2220000000022000000000-2-2200000-2200-220000000
χ272222-2-2-22002-2-222-2-22000-2-22200000000-2-200000000022-2000002i−2i00−2i2i0000000
χ282222-2-2-22002-2-222-2-22000-2-22200000000-2-200000000022-200000−2i2i002i−2i0000000
χ294444444444-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-1004-1-1-1-1-1-1-1-1000000000000000000000
χ304444444444-1-1-1-1-1-1-1-1-4-44-1-1-1-11111111100-4-1-1-1-11111000000000000000000000
χ3144444444-4-4-1-1-1-1-1-1-1-144-4-1-1-1-1-1-1-1-1-1-1-1-100-411111111000000000000000000000
χ3244444444-4-4-1-1-1-1-1-1-1-1-4-4-4-1-1-1-1111111110041111-1-1-1-1000000000000000000000
χ33444444-4-444-1-1-1-1-1-1-1-100-411115555−5−5−5−5000-1-11155−5−5000000000000000000000
χ34444444-4-444-1-1-1-1-1-1-1-100-41111−5−5−5−55555000-1-111−5−555000000000000000000000
χ35444444-4-4-4-4-1-1-1-1-1-1-1-100411115555−5−5−5−500011-1-1−5−555000000000000000000000
χ36444444-4-4-4-4-1-1-1-1-1-1-1-10041111−5−5−5−5555500011-1-155−5−5000000000000000000000
χ3744-4-44-400004-4-4-4-4444000000000000000000000000000004i−4i0000000000000000
χ3844-4-44-400004-4-4-4-444400000000000000000000000000000−4i4i0000000000000000
χ3944-4-4-44004i−4i444-4-4-4-440000000000000000004i−4i000000000000000000000000000
χ4044-4-4-44004i−4i-1-1-11111-10005−55−5−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18000−iii5−i5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19000000000000000000000
χ4144-4-4-44004i−4i-1-1-11111-10005−55−5ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18000−iii5−i5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19000000000000000000000
χ4244-4-4-44004i−4i-1-1-11111-1000−55−55−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18000−ii−i5i5−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19000000000000000000000
χ4344-4-4-44004i−4i-1-1-11111-1000−55−55ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18000−ii−i5i5ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19000000000000000000000
χ4444-4-4-4400−4i4i444-4-4-4-44000000000000000000−4i4i000000000000000000000000000
χ4544-4-4-4400−4i4i-1-1-11111-10005−55−5−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18000i−i−i5i5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19000000000000000000000
χ4644-4-4-4400−4i4i-1-1-11111-10005−55−5ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18000i−i−i5i5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19000000000000000000000
χ4744-4-4-4400−4i4i-1-1-11111-1000−55−55−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18000i−ii5−i5ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19000000000000000000000
χ4844-4-4-4400−4i4i-1-1-11111-1000−55−55ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18000i−ii5−i5−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19000000000000000000000
χ494-44-40000004004-400-42i−2i000002i−2i2i−2i2i−2i2i−2i4-40000000000000002i−2i0000000000000
χ504-44-40000004004-400-42i−2i000002i−2i2i−2i2i−2i2i−2i-44000000000000000−2i2i0000000000000
χ514-44-40000004004-400-4−2i2i00000−2i2i−2i2i−2i2i−2i2i4-4000000000000000−2i2i0000000000000
χ524-44-40000004004-400-4−2i2i00000−2i2i−2i2i−2i2i−2i2i-440000000000000002i−2i0000000000000
χ538888-8-88-800-222-2-222-2000-2-2220000000000000000000000000000000000000000
χ548888-8-8-8800-222-2-222-200022-2-20000000000000000000000000000000000000000
χ5588-8-88-80000-22222-2-2-200025−25−25250000000000000000000000000000000000000000
χ5688-8-88-80000-22222-2-2-2000−252525−250000000000000000000000000000000000000000
χ578-88-8000000-225−25-2225−2524i−4i00000−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ588-88-8000000-225−25-2225−252−4i4i000002ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ598-88-8000000-2−2525-22−252524i−4i00000−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ608-88-8000000-2−2525-22−25252−4i4i000002ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ618-8-88000000800-8800-800000000000000000000000000000000000000000000000
χ628-8-88000000-225−252-2−2525200000002ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000
χ638-8-88000000-225−252-2−252520000000−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000
χ648-8-88000000-2−25252-225−2520000000−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000
χ658-8-88000000-2−25252-225−25200000002ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000

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