Finite Group Databasebeta

← Group #14278556

Character table — Group #14278556

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222444444444444444444448888888888888888881010101016161616161616161616161616161620202020202020202020808080120120120120120120120120
order1223446664451010101212121212121515303030303030202020202020606060606060606060606060888841212202020206060606060606060882424242424242424412121616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i
χ9222222222-2-22222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-20000000000000002-22222-2-2-2-200000000000
χ10222222222-2-22222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222000000000000000-22-2-2-2-2222200000000000
χ11222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-100000000
χ12222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-211-2-2-2-21111111122-1-1-1-1-1-1-1-1-21100000000
χ13222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-1-12222-1-1-1-1-1-1-1-1-2-211111111-21100000000
χ14222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211-2-2-2-211111111-2-2111111112-1-100000000
χ15222-122-1-1-1-2-222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111111122-2-20−i3i30000−i3−i3−i3−i3i3i3i3i32-2-1-1-1-111110−i3i300000000
χ16222-122-1-1-1-2-222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111111122-2-20i3−i30000i3i3i3i3−i3−i3−i3−i32-2-1-1-1-111110i3−i300000000
χ17222-122-1-1-1-2-222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-2-2220−i3i30000−i3−i3−i3−i3i3i3i3i3-221111-1-1-1-10i3−i300000000
χ18222-122-1-1-1-2-222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-2-2220i3−i30000i3i3i3i3−i3−i3−i3−i3-221111-1-1-1-10−i3i300000000
χ1922-222-22-2-20022-2-200002-22222-2-2-2-22-2000022-2-20000000000220000000000000000-2000022-2-2000−i2i2−i2i20000
χ2022-222-22-2-20022-2-200002-22222-2-2-2-22-2000022-2-20000000000220000000000000000-2000022-2-2000i2−i2i2−i20000
χ2122-222-22-2-20022-2-200002-22222-2-2-2-22-2000022-2-20000000000-2-2000000000000000020000-2-2220002−2−220000
χ2222-222-22-2-20022-2-200002-22222-2-2-2-22-2000022-2-20000000000-2-2000000000000000020000-2-222000−222−20000
χ2322-22-222-2-20022-2-20000-222222-2-2-2-2-220000-2-222000000002200000000000000000-2022-2-200000000000−i2i2−i2i2
χ2422-22-222-2-20022-2-20000-222222-2-2-2-2-220000-2-222000000002200000000000000000-2022-2-200000000000i2−i2i2−i2
χ2522-22-222-2-20022-2-20000-222222-2-2-2-2-220000-2-22200000000-2-20000000000000000020-2-222000000000002−2−22
χ2622-22-222-2-20022-2-20000-222222-2-2-2-2-220000-2-22200000000-2-20000000000000000020-2-22200000000000−222−2
χ2744444444444-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000444-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ2844444444444-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4111111111111000000000000000000000
χ29444444444-4-4-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111110000000−5−555−5−555−5−555000000000000000000000
χ30444444444-4-4-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111000000055−5−555−5−555−5−5000000000000000000000
χ314444-4-44440044440000-4-444444444-4-40000-4-4-4-4000000000000000000000000000000000000000000000000
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χ334444-4-444400-1-1-1-10000-4-4-1-1-1-1-1-1-1-111−5−5551111−5−5−5−555550000000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116000000000000000000000
χ344444-4-444400-1-1-1-10000-4-4-1-1-1-1-1-1-1-11155−5−511115555−5−5−5−50000000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116000000000000000000000
χ354444-4-444400-1-1-1-10000-4-4-1-1-1-1-1-1-1-11155−5−511115555−5−5−5−50000000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116000000000000000000000
χ36444-244-2-2-244-1-1-1-1-2-2-2-2-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15200004-2-2-1-1-1-11−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i152000000000000000000000
χ37444-244-2-2-244-1-1-1-1-2-2-2-2-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000-4221111−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152000000000000000000000
χ38444-244-2-2-244-1-1-1-1-2-2-2-2-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15200004-2-2-1-1-1-11+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i152000000000000000000000
χ39444-244-2-2-244-1-1-1-1-2-2-2-2-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000-4221111−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152000000000000000000000
χ40444-244-2-2-2-4-4-1-1-1-12222-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-111111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i15200000−2i32i355−5−5ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116000000000000000000000
χ41444-244-2-2-2-4-4-1-1-1-12222-2-21−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-111111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000002i3−2i3−5−555−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116000000000000000000000
χ42444-244-2-2-2-4-4-1-1-1-12222-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-111111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i15200000−2i32i3−5−555ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92000000000000000000000
χ43444-244-2-2-2-4-4-1-1-1-12222-2-21+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-111111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000002i3−2i355−5−5−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92000000000000000000000
χ44444-2-4-4-2-2-2004444−2i3−2i32i32i322-2-2-2-2-2-2-2-2-4-400002222−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000
χ45444-2-4-4-2-2-20044442i32i3−2i3−2i322-2-2-2-2-2-2-2-2-4-4000022222i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000
χ46444-2-4-4-2-2-200-1-1-1-1−2i3−2i32i32i3221−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521155−5−5−1+i152−1−i152−1+i152−1−i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ920000000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ116000000000000000000000
χ47444-2-4-4-2-2-200-1-1-1-1−2i3−2i32i32i3221−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521155−5−5−1+i152−1−i152−1+i152−1−i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ920000000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116000000000000000000000
χ48444-2-4-4-2-2-200-1-1-1-1−2i3−2i32i32i3221+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15211−5−555−1−i152−1+i152−1−i152−1+i152ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ1160000000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92000000000000000000000
χ49444-2-4-4-2-2-200-1-1-1-1−2i3−2i32i32i3221+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15211−5−555−1−i152−1+i152−1−i152−1+i152ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ1160000000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ116ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.