Finite Group Databasebeta

← Group #14281361

Character table — Group #14281361

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222444444444444444888888888888888888881010101010101010101020202020202020242424242424242424244040404040404040404040406060606060606060120120
order12222222366625666666101010101010101010101015303030303030303030303030303030444444121212124121212121212241010101020202020888824242424242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii11
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−i−iii−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-1
χ10111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-1
χ11111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii-11
χ12111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i-11
χ13111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-11
χ14111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-11
χ15111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-11-1
χ16111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-11111-111-1-1-11111-1-111-1-1-1-1111-1
χ1722222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-100000000002222-1-1-1-1-1-1-1-10000000000
χ1822222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-10000000000-2-2-2-2111111110000000000
χ1922222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-211111100000000002i2i−2i−2i−i−i−i−iiiii0000000000
χ2022222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-21111110000000000−2i−2i2i2iiiii−i−i−i−i0000000000
χ21222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-11100000000002i−2i2i−2i−i−iii−i−iii0000000000
χ22222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-1110000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ23222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-100000000002-2-22-1-11111-1-10000000000
χ24222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-10000000000-222-211-1-1-1-1110000000000
χ252222-2-2222222-22-2-222-2-222-2-2-2-2222-2-22222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2-222-2-22200000000000000000000000000000000
χ262222-2-2222222-22-2-222-2-222-2-2-2-2222-2-22222-2-2-2-22222-2-2-2-2-2-222-2-222222-2-222-2-200000000000000000000000000000000
χ272222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-1111122-2-2221111-2-1-111-1-1000000000000003−33−33−33−30000000000
χ282222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-1111122-2-2221111-2-1-111-1-100000000000000−33−33−33−330000000000
χ292222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-11111-2-222-2-2-1-1-1-1211-1-11100000000000000−i3i3−i3i3i3−i3i3−i30000000000
χ302222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-11111-2-222-2-2-1-1-1-1211-1-11100000000000000i3−i3i3−i3−i3i3−i3i30000000000
χ312222-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2222222-2-2-2-2-2-2-2-222222222-2-22222-222-2-2-2-200000000000000000000000000000000
χ322222-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-22-2-2222200000000000000000000000000000000
χ332222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-12222-2-2-1-1-1-1-2-1-1111100000000000000−i3i3i3−i3−i3i3i3−i30000000000
χ342222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-12222-2-2-1-1-1-1-2-1-1111100000000000000i3−i3−i3i3i3−i3−i3i30000000000
χ352222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-1-2-2-2-2221111211-1-1-1-1000000000000003−3−33−333−30000000000
χ362222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-1-2-2-2-2221111211-1-1-1-100000000000000−333−33−3−330000000000
χ3722-2-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-200000000002i−2i2i−2i2i2i−2i−2i000002i−2i000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ3822-2-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-200000000002i−2i2i−2i2i2i−2i−2i000002i−2i0000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000
χ3922-2-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-20000000000−2i2i−2i2i−2i−2i2i2i00000−2i2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000
χ4022-2-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-20000000000−2i2i−2i2i−2i−2i2i2i00000−2i2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ4122-2-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-22200000000002i−2i−2i2i2i2i−2i−2i00000−2i2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900
χ4222-2-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-22200000000002i−2i−2i2i2i2i−2i−2i00000−2i2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ4322-2-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-2220000000000−2i2i2i−2i−2i−2i2i2i000002i−2i0000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ4422-2-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-2220000000000−2i2i2i−2i−2i−2i2i2i000002i−2i00000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900
χ454444444444444-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000044-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444444-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-4-4111111110000000000000000000000
χ47444444-4-44444-4-144-4-4-4-4-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000000004-4-1-1-1-111110000000000000000000000
χ48444444-4-44444-4-144-4-4-4-4-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000-441111-1-1-1-10000000000000000000000
χ494444-4-4444444-4-1-4-444-4-4-1-11111-1-1-111-1-1-1-11111-1-1-1-111110000000000000000000−5−555−5−5550000000000000000000000
χ504444-4-4444444-4-1-4-444-4-4-1-11111-1-1-111-1-1-1-11111-1-1-1-11111000000000000000000055−5−555−5−50000000000000000000000
χ514444-4-4-4-444444-1-4-4-4-444-1-11111-111-1-1-1-1-1-111111111-1-1-1-10000000000000000000−5−55555−5−50000000000000000000000
χ524444-4-4-4-444444-1-4-4-4-444-1-11111-111-1-1-1-1-1-111111111-1-1-1-1000000000000000000055−5−5−5−5550000000000000000000000
χ5344-4-44-400-2-22204-2200004-444-4-4-40000-2-222-2-22200000000004i−4i4i−4i−2i−2i2i2i00000−2i2i00000000000000000000000000000000
χ5444-4-44-400-2-22204-2200004-444-4-4-40000-2-222-2-2220000000000−4i4i−4i4i2i2i−2i−2i000002i−2i00000000000000000000000000000000
χ5544-4-4-4400-2-222042-200004-4-4-444-40000-2-22222-2-200000000004i−4i−4i4i−2i−2i2i2i000002i−2i00000000000000000000000000000000
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χ714-4-4400-444-44-40-100-440011−55−55-11-15−5-111-1−55−5511-1-15−55−50000000000000000000ζ4−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+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−ζ1160000000000000000000000
χ724-4-4400-444-44-40-100-440011−55−55-11-15−5-111-1−55−5511-1-15−55−50000000000000000000−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−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+ζ1160000000000000000000000
χ734-4-4400-444-44-40-100-4400115−55−5-11-1−55-111-15−55−511-1-1−55−550000000000000000000ζ4+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−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+ζ1160000000000000000000000
χ744-4-4400-444-44-40-100-4400115−55−5-11-1−55-111-15−55−511-1-1−55−550000000000000000000−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+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−ζ1160000000000000000000000
χ754-4-4400-44-22-2204002-200-4-400004-4400-222-2000022-2-2000000000023−23−2323000−23230000000000000000000000000000000000
χ764-4-4400-44-22-2204002-200-4-400004-4400-222-2000022-2-20000000000−232323−2300023−230000000000000000000000000000000000
χ7788888888-4-4-4-48-2-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-211111111111111110000000000000000000000000000000000000000000000000
χ78888888-8-8-4-4-4-4-8-2-4-44444-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000
χ798888-8-888-4-4-4-4-8-244-4-444-2-22222-2-2-2221111-1-1-1-11111-1-1-1-10000000000000000000000000000000000000000000000000
χ808888-8-8-8-8-4-4-4-48-24444-4-4-2-22222-222-2-21111-1-1-1-1-1-1-1-111110000000000000000000000000000000000000000000000000
χ8188-8-88-80088-8-80-28-80000-22-2-22220000-2-222-2-222000000000000000000000000000000000000000000000000000000000
χ8288-8-88-800-4-4440-2-440000-22-2-2222000011-1-111-1-1−i15i15−i15i15−i15i15i15−i150000000000000000000000000000000000000000000000000
χ8388-8-88-800-4-4440-2-440000-22-2-2222000011-1-111-1-1i15−i15i15−i15i15−i15−i15i150000000000000000000000000000000000000000000000000
χ8488-8-8-880088-8-80-2-880000-2222-2-220000-2-22222-2-2000000000000000000000000000000000000000000000000000000000
χ8588-8-8-8800-4-4440-24-40000-2222-2-22000011-1-1-1-111−i15i15−i15i15i15−i15−i15i150000000000000000000000000000000000000000000000000
χ8688-8-8-8800-4-4440-24-40000-2222-2-22000011-1-1-1-111i15−i15i15−i15−i15i15i15−i150000000000000000000000000000000000000000000000000
χ878-88-800008-8-880-20000002-2−252525−2520000-22-22−252525−25000000000000000000000000000000000000000000000000000000000
χ888-88-800008-8-880-20000002-225−25−252520000-22-2225−25−2525000000000000000000000000000000000000000000000000000000000
χ898-88-80000-444-40-20000−4i34i32-2−252525−25200001-11-15−5−55i15−i15−i15i15i3i3−i3−i30000000000000000000000000000000000000000000000000
χ908-88-80000-444-40-20000−4i34i32-225−25−2525200001-11-1−555−5−i15i15i15−i15i3i3−i3−i30000000000000000000000000000000000000000000000000
χ918-88-80000-444-40-200004i3−4i32-2−252525−25200001-11-15−5−55−i15i15i15−i15−i3−i3i3i30000000000000000000000000000000000000000000000000
χ928-88-80000-444-40-200004i3−4i32-225−25−2525200001-11-1−555−5i15−i15−i15i15−i3−i3i3i30000000000000000000000000000000000000000000000000
χ938-8-88008-8-44-440-200-440022−2525−2525-2-22−25251-1-115−55−511-1-15−55−50000000000000000000000000000000000000000000000000
χ948-8-88008-8-44-440-200-44002225−2525−25-2-2225−251-1-11−55−5511-1-1−55−550000000000000000000000000000000000000000000000000
χ958-8-8800-88-44-440-2004-40022−2525−2525-22-225−251-1-115−55−5-1-111−55−550000000000000000000000000000000000000000000000000
χ968-8-8800-88-44-440-2004-4002225−2525−25-22-2−25251-1-11−55−55-1-1115−55−50000000000000000000000000000000000000000000000000

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