Finite Group Databasebeta

← Group #13020532

Character table — Group #13020532

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111224444444444448888888888888881010161616161616161616202020202040404040404040404040408080808080
order12222222225101010101010102241010101010101010101010104441010202020202020444442248888888848888
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
χ5111111111111111111-1-111111-1-1-1-1-1-1-1-111-11111-1-1-1-111111-1-1111111111-1-1-1-1-1
χ6111111111111111111-1-111111-1-1-1-1-1-1-1-111-11111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1−i−i−i−iiiii1ii−i−i
χ911111111-1-11111111111-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-111-1-111-1-1-11-11-1
χ1011111111-1-11111111111-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-111-1-111-1-11-11
χ1111111111-1-11111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11ii−i−i−i−iii1i−i−ii
χ1211111111-1-11111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11−i−iiiii−i−i1−iii−i
χ1311111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-111-1-1-111-1-111-1-11-11-11
χ1411111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-111-1-1-1-1-111-1-11111-11-1
χ1511111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111-1-1111ii−i−i−i−iii-1−iii−i
χ1611111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111-1-1111−i−iiiii−i−i-1i−i−ii
χ17222222-2-2222222222200-2-2-2-2-20000000022022-2-20000222-2-200-20000000000000
χ18222222-2-2222222222200-2-2-2-2-200000000-2-2022-2-20000-2-2-2220020000000000000
χ19222222-2-2-2-222222222002-2-2-2-200000000220-2-22200002-2-2-2-20020000000000000
χ20222222-2-2-2-222222222002-2-2-2-200000000-2-20-2-2220000-2222200-20000000000000
χ212222-2-22-200222-2-22-2-200022-2-20000000022000000000-2002-2000002-2002-200000
χ222222-2-22-200222-2-22-2-200022-2-20000000022000000000-2002-200000-2200-2200000
χ232222-2-22-200222-2-22-2-200022-2-200000000-2-2000000000200-22000002i−2i00−2i2i00000
χ242222-2-22-200222-2-22-2-200022-2-200000000-2-2000000000200-2200000−2i2i002i−2i00000
χ252222-2-2-2200222-2-22-2-2000-2-2220000000022000000000-200-220002-2002-20000000
χ262222-2-2-2200222-2-22-2-2000-2-2220000000022000000000-200-22000-2200-220000000
χ272222-2-2-2200222-2-22-2-2000-2-22200000000-2-20000000002002-20002i−2i00−2i2i0000000
χ282222-2-2-2200222-2-22-2-2000-2-22200000000-2-20000000002002-2000−2i2i002i−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
χ3744-4-44-400004-4-4444-4-40000000000000000000000000004i−4i000000000000000000
χ3844-4-44-400004-4-4444-4-4000000000000000000000000000−4i4i000000000000000000
χ3944-4-4-44004-44-4-4-4-44440000000000000000004-4000000000000000000000000000
χ4044-4-4-44004-4-11111-1-1-10005−55−5−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−ζ18000-115−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18000000000000000000000
χ4144-4-4-44004-4-11111-1-1-10005−55−5ζ2−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+ζ18000-115−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18000000000000000000000
χ4244-4-4-44004-4-11111-1-1-1000−55−55−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+ζ18000-11−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000000000000
χ4344-4-4-44004-4-11111-1-1-1000−55−55ζ2+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−ζ18000-11−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18000000000000000000000
χ4444-4-4-4400-444-4-4-4-4444000000000000000000-44000000000000000000000000000
χ4544-4-4-4400-44-11111-1-1-10005−55−5−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−ζ180001-1−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18000000000000000000000
χ4644-4-4-4400-44-11111-1-1-10005−55−5ζ2−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+ζ180001-1−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18000000000000000000000
χ4744-4-4-4400-44-11111-1-1-1000−55−55−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+ζ180001-15−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18000000000000000000000
χ4844-4-4-4400-44-11111-1-1-1000−55−55ζ2+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−ζ180001-15−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000000000000
χ494-4-4400000044-400-4002-2000002-22-22-22-24-4000000000000002-200000000000000
χ504-4-4400000044-400-4002-2000002-22-22-22-2-4400000000000000-2200000000000000
χ514-4-4400000044-400-400-2200000-22-22-22-224-400000000000000-2200000000000000
χ524-4-4400000044-400-400-2200000-22-22-22-22-44000000000000002-200000000000000
χ538888-8-88-800-2-2-222-222000-2-2220000000000000000000000000000000000000000
χ548888-8-8-8800-2-2-222-22200022-2-20000000000000000000000000000000000000000
χ5588-8-88-80000-222-2-2-22200025−25−25250000000000000000000000000000000000000000
χ5688-8-88-80000-222-2-2-222000−252525−250000000000000000000000000000000000000000
χ578-88-80000008-8800-80000000000000000000000000000000000000000000000000
χ588-88-8000000-22-225−25225−2500000002ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000
χ598-88-8000000-22-225−25225−250000000−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000
χ608-88-8000000-22-2−25252−25250000000−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000
χ618-88-8000000-22-2−25252−252500000002ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000
χ628-8-88000000-2-2225−252−25254-400000−1−51+5−1−51+5−1+51−5−1+51−500000000000000000000000000000000
χ638-8-88000000-2-2225−252−2525-44000001+5−1−51+5−1−51−5−1+51−5−1+500000000000000000000000000000000
χ648-8-88000000-2-22−2525225−254-400000−1+51−5−1+51−5−1−51+5−1−51+500000000000000000000000000000000
χ658-8-88000000-2-22−2525225−25-44000001−5−1+51−5−1+51+5−1−51+5−1−500000000000000000000000000000000

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