Finite Group Databasebeta

← Group #14278081

Character table — Group #14278081

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444448888888888888888888888888888888888888888888882020202040404040404040404040120120120120120120120120
order1222223666666651010101010101015153030303030303030303030303030224666610101010101010101212202020203030303030303030303030303030303060606060606060602244446612121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111ii−i−i−i−iii
χ811111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111−i−iiiii−i−i
χ92222222222222222222222222222222222222200-2000000000000-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-222-2-20022-2-2000000000000
χ102222222222222222222222222222222222222200-2000000000000-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-22200-2-222000000000000
χ11222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2−i3−i3i3i30000000011-2-2-2-2−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i31111111122-2-200-1-111−i3−i3i3i300000000
χ12222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2−i3−i3i3i30000000011-2-2-2-2−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i311111111-2-2220011-1-1i3i3−i3−i300000000
χ13222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2i3i3−i3−i30000000011-2-2-2-2i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i31111111122-2-200-1-111i3i3−i3−i300000000
χ14222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2i3i3−i3−i30000000011-2-2-2-2i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i311111111-2-2220011-1-1−i3−i3i3i300000000
χ15222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ16222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ17222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-221111-2-2-2-2-2-2-2-2-1-122221111111111111111-1-1-1-1-1-1-1-12222-2-2-1-1-1-1111100000000
χ18222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-221111-2-2-2-2-2-2-2-2-1-122221111111111111111-1-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-100000000
χ1922-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000002i−2i00002i−2i00001+i−1−i1−i−1+i0000
χ2022-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000002i−2i00002i−2i0000−1−i1+i−1+i1−i0000
χ2122-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000−2i2i0000−2i2i00001−i−1+i1+i−1−i0000
χ2222-2-22-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000−2i2i0000−2i2i0000−1+i1−i−1−i1+i0000
χ2322-2-2-2222-2-2-222-222-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000000002-200002-20000000000−i2i2−i2i2
χ2422-2-2-2222-2-2-222-222-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000000002-200002-20000000000i2−i2i2−i2
χ2522-2-2-2222-2-2-222-222-2-222-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000-220000-2200000000002−2−22
χ2622-2-2-2222-2-2-222-222-2-222-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000-220000-220000000000−222−2
χ2744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-40000−5−5−5−55555-4-41111−5−5−5−55555−5−5−5−55555111111110000000000000000000000
χ2844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-400005555−5−5−5−5-4-411115555−5−5−5−55555−5−5−5−5111111110000000000000000000000
χ2944444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-44-4-4-4-41111111144-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000000000000000000000
χ31444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i15200-4−2i3−2i32i32i3−5−5−5−55555221111ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1520000000000000000000000
χ32444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i15200-42i32i3−2i3−2i35555−5−5−5−5221111−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1520000000000000000000000
χ33444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i152444-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1-1-11+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1520000000000000000000000
χ34444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i152-4-44222211111111-2-2-1-1-1-1−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1520000000000000000000000
χ35444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i15200-4−2i3−2i32i32i35555−5−5−5−5221111ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1520000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i15200-42i32i3−2i3−2i3−5−5−5−55555221111−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1520000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i152444-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1-1-11−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1520000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i152-4-44222211111111-2-2-1-1-1-1−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1520000000000000000000000
χ394444-4-444-4-44-4-4444-4-4-4-4444444-4-4-4-4-4-4-4-444440000000000000000000000000000000000000000000000000000000000000000000
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χ904-4-4400-22−2i32i322i3−2i3-24-400004-4-2-222−2i32i32i3−2i32i3−2i3−2i32i3-2-22200000000000000000000000000000000000000000000000002-20000−1+i31−i3−1−i31+i300000000
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χ9488-8-88-88888-8-8-8-8-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-88-8-4-4-4-44444-2-2-2-222221−i151+i151−i151+i151−i151−i151+i151+i15−1+i15−1+i15−1−i15−1−i15−1+i15−1−i15−1+i15−1−i150000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-88-8-4-4-4-44444-2-2-2-222221+i151−i151+i151−i151+i151+i151−i151−i15−1−i15−1−i15−1+i15−1+i15−1−i15−1+i15−1−i15−1+i150000000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-8888-8-8-888-8-2-222-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-88-4-4444-4-44-2-222-2-2221−i151+i151−i151+i15−1+i15−1+i15−1−i15−1−i151−i151−i151+i151+i15−1+i15−1−i15−1+i15−1−i150000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-88-4-4444-4-44-2-222-2-2221+i151−i151+i151−i15−1−i15−1−i15−1+i15−1+i151+i151+i151−i151−i15−1−i15−1+i15−1−i15−1+i150000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-800-8008-22−252525−25-22-2-222−2525−252525−2525−25-2-2220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88008-800-8008-2225−25−2525-22-2-22225−2525−25−2525−2525-2-2220000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-44−4i34i344i3−4i3-4-22−252525−25-221+i151−i15−1−i15−1+i152ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ922ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ1161+i151−i15−1−i15−1+i150000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-8800-44−4i34i344i3−4i3-4-2225−25−2525-221−i151+i15−1+i15−1−i152ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ921−i151+i15−1+i15−1−i150000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-8800-444i3−4i34−4i34i3-4-22−252525−25-221−i151+i15−1+i15−1−i15−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ922ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ921−i151+i15−1+i15−1−i150000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-8800-444i3−4i34−4i34i3-4-2225−25−2525-221+i151−i15−1−i15−1+i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ922ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1161+i151−i15−1−i15−1+i150000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.