Finite Group Databasebeta

← Group #14314964

Character table — Group #14314964

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444448888888888888888888888101010101212121220202020202024242424242424243030303040404040404040404040404040406060120120120120
order1244234612125688101010122020202015242430303040404040606060601201201201201201201201208888448844242424242020202040404040888812121616161648484848484848482416161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1ii−i−i
χ611111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1−i−iii
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−iiiii−i−i−i−i11−i−iii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iii−i−i−i−iiiii11ii−i−i
χ9111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-11-11-111-1-111-1-1-1-11-11-1
χ10111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-11-11-1-111-1-111-1-1-11-11
χ11111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-111-11-11
χ12111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-111111-11-1
χ13111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111i−i−iiii−i−i−i−iii11i−i−ii
χ14111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111−iii−i−i−iiiii−i−i11−iii−i
χ15111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111i−i−iiii−i−i−i−iii-1-1−iii−i
χ16111111111111-1-1111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111−iii−i−i−iiiii−i−i-1-1i−i−ii
χ1722222-12-1-1-12-122222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1000000000000-1-12222-1-1-1-1-1-1-1-1000000
χ1822222-12-1-1-12-122222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1000000000000-1-1-2-2-2-211111111000000
χ1922222-12-1-1-12-122222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-21111000000000000112i2i−2i−2i−i−i−i−iiiii000000
χ2022222-12-1-1-12-122222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2111100000000000011−2i−2i2i2iiiii−i−i−i−i000000
χ2122222-12-1-1-12-1-2-2222-12222-111-1-1-1-2-2-2-2-1-1-1-11111111122220000-2-2-1-1-1-1000000000000112-22-2-1-111-1-111000000
χ2222222-12-1-1-12-1-2-2222-12222-111-1-1-1-2-2-2-2-1-1-1-11111111122220000-2-2-1-1-1-100000000000011-22-2211-1-111-1-1000000
χ2322222-12-1-1-12-1-2-2222-12222-111-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-20000221111000000000000-1-12i−2i−2i2i−i−iiiii−i−i000000
χ2422222-12-1-1-12-1-2-2222-12222-111-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-20000221111000000000000-1-1−2i2i2i−2iii−i−i−i−iii000000
χ252222-22-22222-22i−2i2-2-2-2-2-22222i−2i-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i22-2-200002i−2i22-2-20000000000002i−2i000000000000000000
χ262222-22-22222-22i−2i2-2-2-2-2-22222i−2i-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i-2-2220000−2i2i-2-222000000000000−2i2i000000000000000000
χ272222-22-22222-2−2i2i2-2-2-2-2-2222−2i2i-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i22-2-20000−2i2i22-2-2000000000000−2i2i000000000000000000
χ282222-22-22222-2−2i2i2-2-2-2-2-2222−2i2i-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i-2-22200002i−2i-2-2220000000000002i−2i000000000000000000
χ292222-2-1-2-1-1-1212i−2i2-2-21-2-222-1−ii11-12i2i−2i−2i-1-111−i−i−i−iiiii22-2-200002i−2i-1-111000000000000−ii0000−i3i33−3−i3i33−3000000
χ302222-2-1-2-1-1-1212i−2i2-2-21-2-222-1−ii11-12i2i−2i−2i-1-111−i−i−i−iiiii22-2-200002i−2i-1-111000000000000−ii0000i3−i3−33i3−i3−33000000
χ312222-2-1-2-1-1-1212i−2i2-2-21-2-222-1−ii11-12i2i−2i−2i-1-111−i−i−i−iiiii-2-2220000−2i2i11-1-1000000000000i−i00003−3i3−i3−33−i3i3000000
χ322222-2-1-2-1-1-1212i−2i2-2-21-2-222-1−ii11-12i2i−2i−2i-1-111−i−i−i−iiiii-2-2220000−2i2i11-1-1000000000000i−i0000−33−i3i33−3i3−i3000000
χ332222-2-1-2-1-1-121−2i2i2-2-21-2-222-1i−i11-1−2i−2i2i2i-1-111iiii−i−i−i−i22-2-20000−2i2i-1-111000000000000i−i0000−i3i3−33−i3i3−33000000
χ342222-2-1-2-1-1-121−2i2i2-2-21-2-222-1i−i11-1−2i−2i2i2i-1-111iiii−i−i−i−i22-2-20000−2i2i-1-111000000000000i−i0000i3−i33−3i3−i33−3000000
χ352222-2-1-2-1-1-121−2i2i2-2-21-2-222-1i−i11-1−2i−2i2i2i-1-111iiii−i−i−i−i-2-22200002i−2i11-1-1000000000000−ii00003−3−i3i3−33i3−i3000000
χ362222-2-1-2-1-1-121−2i2i2-2-21-2-222-1i−i11-1−2i−2i2i2i-1-111iiii−i−i−i−i-2-22200002i−2i11-1-1000000000000−ii0000−33i3−i33−3−i3i3000000
χ3722-2-222-22-2-22200222-2-2-2-2-22002220000-2-2-2-2000000002i−2i2i−2i002i−2i002i−2i2i−2i00002i2i−2i−2i0000000000000000002-20000
χ3822-2-222-22-2-22200222-2-2-2-2-22002220000-2-2-2-2000000002i−2i2i−2i00−2i2i002i−2i2i−2i0000−2i−2i2i2i000000000000000000-220000
χ3922-2-222-22-2-22200222-2-2-2-2-22002220000-2-2-2-200000000−2i2i−2i2i002i−2i00−2i2i−2i2i00002i2i−2i−2i000000000000000000-220000
χ4022-2-222-22-2-22200222-2-2-2-2-22002220000-2-2-2-200000000−2i2i−2i2i00−2i2i00−2i2i−2i2i0000−2i−2i2i2i0000000000000000002-20000
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χ4322-2-2-2222-2-22-2002-2-2222-2-2200-2-220000-2-22200000000−2i2i2i−2i2i−2i0000−2i2i2i−2i2i2i−2i−2i0000-2-22200000000000000000000
χ4422-2-2-2222-2-22-2002-2-2222-2-2200-2-220000-2-22200000000−2i2i2i−2i−2i2i0000−2i2i2i−2i−2i−2i2i2i000022-2-200000000000000000000
χ454444444444-1444-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100004444000000-1-1-1-1-1-1-1-1000000000000000000000000
χ464444444444-1444-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4-400000011111111000000000000000000000000
χ474444444444-14-4-4-1-1-14-1-1-1-1-1-4-4-1-1-11111-1-1-1-111111111000044-4-4000000-1-1-1-11111000000000000000000000000
χ484444444444-14-4-4-1-1-14-1-1-1-1-1-4-4-1-1-11111-1-1-1-1111111110000-4-4440000001111-1-1-1-1000000000000000000000000
χ494444-44-4444-1-44i−4i-111-411-1-1-14i−4i11-1−i−iii-1-111−i−i−i−iiiii00000000000000−i5i5−i5i5−55−55000000000000000000000000
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χ514444-44-4444-1-4−4i4i-111-411-1-1-1−4i4i11-1ii−i−i-1-111iiii−i−i−i−i00000000000000−i5i5−i5i55−55−5000000000000000000000000
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χ5344-4-444-44-4-4-1400-1-1-1-41111-100-1-1-1−i5i5−i5i51111−i5−i5i5i5−i5−i5i5i50000004i−4i000000−555−5−i−iii000000000000000000000000
χ5444-4-444-44-4-4-1400-1-1-1-41111-100-1-1-1−i5i5−i5i51111−i5−i5i5i5−i5−i5i5i5000000−4i4i0000005−5−55ii−i−i000000000000000000000000
χ5544-4-444-44-4-4-1400-1-1-1-41111-100-1-1-1i5−i5i5−i51111i5i5−i5−i5i5i5−i5−i50000004i−4i0000005−5−55−i−iii000000000000000000000000
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χ888-8−8i8i0-4044i−4i-20002−252502i5−2i52i−2i1005−5-10000−ii−i5i5ζ7+ζ23+ζ29−ζ47+ζ61−ζ101−ζ103−ζ109−ζ7−ζ23−ζ29+ζ47−ζ61+ζ101+ζ103+ζ109ζ13+ζ31−ζ37−ζ53−ζ71+ζ77−ζ79+ζ119−ζ13−ζ31+ζ37+ζ53+ζ71−ζ77+ζ79−ζ119−ζ7−ζ23+ζ29+ζ47+ζ61−ζ101+ζ103−ζ109ζ7+ζ23−ζ29−ζ47−ζ61+ζ101−ζ103+ζ109−ζ13+ζ31+ζ37+ζ53−ζ71−ζ77−ζ79+ζ119ζ13−ζ31−ζ37−ζ53+ζ71+ζ77+ζ79−ζ1190000000000000000000000000000000000000000000000
χ898-8−8i8i0-4044i−4i-2000225−250−2i52i52i−2i100−55-10000−iii5−i5−ζ13−ζ31+ζ37+ζ53+ζ71−ζ77+ζ79−ζ119ζ13+ζ31−ζ37−ζ53−ζ71+ζ77−ζ79+ζ119ζ7+ζ23+ζ29−ζ47+ζ61−ζ101−ζ103−ζ109−ζ7−ζ23−ζ29+ζ47−ζ61+ζ101+ζ103+ζ109−ζ13+ζ31+ζ37+ζ53−ζ71−ζ77−ζ79+ζ119ζ13−ζ31−ζ37−ζ53+ζ71+ζ77+ζ79−ζ119ζ7+ζ23−ζ29−ζ47−ζ61+ζ101−ζ103+ζ109−ζ7−ζ23+ζ29+ζ47+ζ61−ζ101+ζ103−ζ1090000000000000000000000000000000000000000000000
χ908-8−8i8i0-4044i−4i-2000225−250−2i52i52i−2i100−55-10000−iii5−i5ζ13+ζ31−ζ37−ζ53−ζ71+ζ77−ζ79+ζ119−ζ13−ζ31+ζ37+ζ53+ζ71−ζ77+ζ79−ζ119−ζ7−ζ23−ζ29+ζ47−ζ61+ζ101+ζ103+ζ109ζ7+ζ23+ζ29−ζ47+ζ61−ζ101−ζ103−ζ109ζ13−ζ31−ζ37−ζ53+ζ71+ζ77+ζ79−ζ119−ζ13+ζ31+ζ37+ζ53−ζ71−ζ77−ζ79+ζ119−ζ7−ζ23+ζ29+ζ47+ζ61−ζ101+ζ103−ζ109ζ7+ζ23−ζ29−ζ47−ζ61+ζ101−ζ103+ζ1090000000000000000000000000000000000000000000000

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