Finite Group Databasebeta

← Group #13085762

Character table — Group #13085762

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122222222244444444444444448888888888881010101010101212121212122020202020202424242424242424242424243636363636606060606060180
order123345566101036121212121515151520203030303015153030606060606060606024661212246612126661212121010202030303030606060608404040402266668
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-1
χ3111111111111111111111111111111111111111111111-11-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11
χ5111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1-1111
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ922222−1−52−1+5222−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000000222222000000−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522−1−52−1−52−1+52−1+520000000
χ1022222−1−52−1+5222−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+520000002-222-2-2000000−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52-21+521+521−521−520000000
χ1122222−1−52−1+5222−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000000-22-2-2220000001+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-21+521+521−521−520000000
χ1222222−1−52−1+5222−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000000-2-2-2-2-2-20000001+521−521+521−521+521+521−521−521+521+521−521−522−1−52−1−52−1+52−1+520000000
χ1322222−1+52−1−5222−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000000222222000000−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522−1+52−1+52−1−52−1−520000000
χ1422222−1+52−1−5222−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−520000002-222-2-2000000−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52-21−521−521+521+520000000
χ1522222−1+52−1−5222−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000000-22-2-2220000001−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-21−521−521+521+520000000
χ1622222−1+52−1−5222−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000000-2-2-2-2-2-20000001−521+521−521+521−521−521+521+521−521−521+521+522−1+52−1+52−1−52−1−520000000
χ172222-222222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-22-222-2-2000000222-2-2-2000000000000000000000000
χ182222-222222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2-22-2-222000000-2-2-2222000000000000000000000000
χ19222-1222-1222-1-1-12-1-122-1-122-1-122-1-1-1-1-1-122-1-1-1-122-1-12220-1-1002-1-1-1-1-12200-1-1-1-10000000002000-1-10
χ20222-1222-1222-1-1-12-1-122-1-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-2011002-1-1-1-1-1-2-2001111000000000-2000110
χ21222-1222-1222-1-1-12-1-122-1-122-1-122-1-1-1-1-1-122-1-1-1-1-2-211-2-220-1-100-2111112200-1-1-1-1000000000-2000110
χ22222-1222-1222-1-1-12-1-122-1-122-1-122-1-1-1-1-1-122-1-1-1-1-2-211-2-2-201100-211111-2-20011110000000002000-1-10
χ23222-1-222-1222-1-11-21122-1-1-2-2-1-122-1-1-1-111-2-211112-2-1-1-2-200−i3i3002-1-11110000−i3i3−i3i30000000000000−i3i30
χ24222-1-222-1222-1-11-21122-1-1-2-2-1-122-1-1-1-111-2-211112-2-1-1-2-200i3−i3002-1-11110000i3−i3i3−i30000000000000i3−i30
χ25222-1-222-1222-1-11-21122-1-1-2-2-1-122-1-1-1-111-2-21111-22112200−i3i300-211-1-1-10000−i3i3−i3i30000000000000i3−i30
χ26222-1-222-1222-1-11-21122-1-1-2-2-1-122-1-1-1-111-2-21111-22112200i3−i300-211-1-1-10000i3−i3i3−i30000000000000−i3i30
χ2722-122222-122-1-12-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-12222-1-10200-1-1-1-1-12-1-100220000-1-1-1-10000002-1-1000
χ2822-122222-122-1-12-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-12222-1-10-20011-1-1-12-1-100-2-200001111000000-211000
χ2922-122222-122-1-12-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2110200-1-1111-21100220000-1-1-1-1000000-211000
χ3022-122222-122-1-12-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2110-20011111-21100-2-2000011110000002-1-1000
χ3122-12-2222-122-1-1-2111-1-122-2-222-1-1-1-1-1-1-2-21111112-222110000−i3i3-1-1-1-21100000000−i3i3−i3i30000000−i3i3000
χ3222-12-2222-122-1-1-2111-1-122-2-222-1-1-1-1-1-1-2-21111112-222110000i3−i3-1-1-1-21100000000i3−i3i3−i30000000i3−i3000
χ3322-12-2222-122-1-1-2111-1-122-2-222-1-1-1-1-1-1-2-2111111-22-2-2-1-10000−i3i31112-1-100000000−i3i3−i3i30000000i3−i3000
χ3422-12-2222-122-1-1-2111-1-122-2-222-1-1-1-1-1-1-2-2111111-22-2-2-1-10000i3−i31112-1-100000000i3−i3i3−i30000000−i3i3000
χ354444-4−1−5−1+544−1−5−1+544-4-4-4-4−1−5−1+5−1−5−1+51+51−5−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+51+51−51+51−51+51+51−51−5000000000000000000000000000000000000000000
χ364444-4−1+5−1−544−1+5−1−544-4-4-4-4−1+5−1−5−1+5−1−51−51+5−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−51−51+51−51+51−51−51+51+5000000000000000000000000000000000000000000
χ37444-24−1−5−1+5-24−1−5−1+5-2-2-24-2-2−1−5−1+51+521−52−1−5−1+51+521−52−1−5−1+51+521−521+521−521+521−52−1−5−1+51+521+521−521−5200000040-2-200000000−1−5−1+5001+521+521−521−520000000000000000
χ38444-24−1−5−1+5-24−1−5−1+5-2-2-24-2-2−1−5−1+51+521−52−1−5−1+51+521−52−1−5−1+51+521−521+521−521+521−52−1−5−1+51+521+521−521−52000000-4022000000001+51−500−1−52−1−52−1+52−1+520000000000000000
χ39444-24−1+5−1−5-24−1+5−1−5-2-2-24-2-2−1+5−1−51−521+52−1+5−1−51−521+52−1+5−1−51−521+521−521+521−521+52−1+5−1−51−521−521+521+5200000040-2-200000000−1+5−1−5001−521−521+521+520000000000000000
χ40444-24−1+5−1−5-24−1+5−1−5-2-2-24-2-2−1+5−1−51−521+52−1+5−1−51−521+52−1+5−1−51−521+521−521+521−521+52−1+5−1−51−521−521+521+52000000-4022000000001−51+500−1+52−1+52−1−52−1−520000000000000000
χ41444-2-4−1−5−1+5-24−1−5−1+5-2-22-422−1−5−1+51+521−521+51−51+521−52−1−5−1+51+521−521+521−52−1−52−1+521+51−5−1−52−1−52−1+52−1+5200000000−2i32i3000000000000ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ1160000000000000000
χ42444-2-4−1−5−1+5-24−1−5−1+5-2-22-422−1−5−1+51+521−521+51−51+521−52−1−5−1+51+521−521+521−52−1−52−1+521+51−5−1−52−1−52−1+52−1+52000000002i3−2i3000000000000−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ1160000000000000000
χ43444-2-4−1+5−1−5-24−1+5−1−5-2-22-422−1+5−1−51−521+521−51+51−521+52−1+5−1−51−521+521−521+52−1+52−1−521−51+5−1+52−1+52−1−52−1−5200000000−2i32i3000000000000ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ920000000000000000
χ44444-2-4−1+5−1−5-24−1+5−1−5-2-22-422−1+5−1−51−521+521−51+51−521+52−1+5−1−51−521+521−521+52−1+52−1−521−51+5−1+52−1+52−1−52−1−52000000002i3−2i3000000000000−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ920000000000000000
χ4544-244−1−5−1+54-2−1−5−1+5-2-24-2-2-21+521−52−1−5−1+5−1−5−1+5−1−5−1+51+521−521+521−521+521−52−1−5−1+51+521−521+521+521−521−520000000400-2-200000000−1−5−1+500001+521+521−521−52000000000000
χ4644-244−1−5−1+54-2−1−5−1+5-2-24-2-2-21+521−52−1−5−1+5−1−5−1+5−1−5−1+51+521−521+521−521+521−52−1−5−1+51+521−521+521+521−521−520000000-40022000000001+51−50000−1−52−1−52−1+52−1+52000000000000
χ4744-244−1+5−1−54-2−1+5−1−5-2-24-2-2-21−521+52−1+5−1−5−1+5−1−5−1+5−1−51−521+521−521+521−521+52−1+5−1−51−521+521−521−521+521+520000000400-2-200000000−1+5−1−500001−521−521+521+52000000000000
χ4844-244−1+5−1−54-2−1+5−1−5-2-24-2-2-21−521+52−1+5−1−5−1+5−1−5−1+5−1−51−521+521−521+521−521+52−1+5−1−51−521+521−521−521+521+520000000-40022000000001−51+50000−1+52−1+52−1−52−1−52000000000000
χ4944-24-4−1−5−1+54-2−1−5−1+5-2-2-42221+521−52−1−5−1+51+51−5−1−5−1+51+521−521+521−521+521−521+51−5−1−52−1+52−1−52−1−52−1+52−1+520000000000−2i32i300000000000000ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116000000000000
χ5044-24-4−1−5−1+54-2−1−5−1+5-2-2-42221+521−52−1−5−1+51+51−5−1−5−1+51+521−521+521−521+521−521+51−5−1−52−1+52−1−52−1−52−1+52−1+5200000000002i3−2i300000000000000−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116000000000000
χ5144-24-4−1+5−1−54-2−1+5−1−5-2-2-42221−521+52−1+5−1−51−51+5−1+5−1−51−521+521−521+521−521+521−51+5−1+52−1−52−1+52−1+52−1−52−1−520000000000−2i32i300000000000000ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92000000000000
χ5244-24-4−1+5−1−54-2−1+5−1−5-2-2-42221−521+52−1+5−1−51−51+5−1+5−1−51−521+521−521+521−521+521−51+5−1+52−1−52−1+52−1+52−1−52−1−5200000000002i3−2i300000000000000−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92000000000000
χ5344-2-2444-2-24411-2-211-2-2-2-244-2-2-2-21111-2-2-2-2111144-2-2-2-2000000-211-211000000000000000000000000
χ5444-2-2444-2-24411-2-211-2-2-2-244-2-2-2-21111-2-2-2-21111-4-422220000002-1-12-1-1000000000000000000000000
χ5544-2-2-444-2-2441122-1-1-2-2-2-2-4-4-2-2-2-211112222-1-1-1-14-4-2-222000000-2112-1-1000000000000000000000000
χ5644-2-2-444-2-2441122-1-1-2-2-2-2-4-4-2-2-2-211112222-1-1-1-1-4422-2-20000002-1-1-211000000000000000000000000
χ574-444044-4-4-4-44-40000444400-4-4-4-444-4-400000000000000000000000000000000000000000000000000
χ584-4440−1−5−1+5-4-41+51−54-40000−1−5−1+5−1−5−1+5001+51−51+51−5−1−5−1+51+51−5000000000000000000000000000000000000000ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ119ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ1190000000
χ594-4440−1−5−1+5-4-41+51−54-40000−1−5−1+5−1−5−1+5001+51−51+51−5−1−5−1+51+51−5000000000000000000000000000000000000000−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ119−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ1190000000
χ604-4440−1+5−1−5-4-41−51+54-40000−1+5−1−5−1+5−1−5001−51+51−51+5−1+5−1−51−51+5000000000000000000000000000000000000000−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ119ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ119−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ1030000000
χ614-4440−1+5−1−5-4-41−51+54-40000−1+5−1−5−1+5−1−5001−51+51−51+5−1+5−1−51−51+5000000000000000000000000000000000000000ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ119−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ119ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ1030000000
χ624-44-20442-4-4-4-22000044-2-20022-4-4-2-2220000000000−2i32i3000000000−2i32i3000000000000000000000000000
χ634-44-20442-4-4-4-22000044-2-20022-4-4-2-22200000000002i3−2i30000000002i3−2i3000000000000000000000000000
χ644-4-24044-42-4-4-220000-2-24400-4-422-2-22200000000000023−23000000000023−23000000000000000000000000
χ654-4-24044-42-4-4-220000-2-24400-4-422-2-222000000000000−23230000000000−2323000000000000000000000000
χ664-4-2-204422-4-41-1003i−3i-2-2-2-200222211-1-100003i−3i3i−3i00−2i32i323−230000000i3−i30−33000000000000000000000000
χ674-4-2-204422-4-41-1003i−3i-2-2-2-200222211-1-100003i−3i3i−3i002i3−2i3−23230000000−i3i303−3000000000000000000000000
χ684-4-2-204422-4-41-100−3i3i-2-2-2-200222211-1-10000−3i3i−3i3i00−2i32i3−23230000000i3−i303−3000000000000000000000000
χ694-4-2-204422-4-41-100−3i3i-2-2-2-200222211-1-10000−3i3i−3i3i002i3−2i323−230000000−i3i30−33000000000000000000000000
χ7088-4-48−2−25−2+25-4-4−2−25−2+2522-4-4221+51−51+51−5−2−25−2+251+51−51+51−5−1−52−1+52−1−52−1+521+51−51+51−5−1−52−1−52−1+52−1+52000000000000000000000000000000000000000000
χ7188-4-48−2+25−2−25-4-4−2+25−2−2522-4-4221−51+51−51+5−2+25−2−251−51+51−51+5−1+52−1−52−1+52−1−521−51+51−51+5−1+52−1+52−1−52−1−52000000000000000000000000000000000000000000
χ7288-4-4-8−2−25−2+25-4-4−2−25−2+252244-2-21+51−51+51−52+252−251+51−51+51−5−1−52−1+52−1−52−1+52−1−5−1+5−1−5−1+51+521+521−521−52000000000000000000000000000000000000000000
χ7388-4-4-8−2+25−2−25-4-4−2+25−2−252244-2-21−51+51−51+52−252+251−51+51−51+5−1+52−1−52−1+52−1−52−1+5−1−5−1+5−1−51−521−521+521+52000000000000000000000000000000000000000000
χ748-88-40−2−25−2+254-82+252−25-440000−2−25−2+251+51−500−1−5−1+52+252−251+51−5−1−5−1+500000000000000000000000000000000000000000000000000
χ758-88-40−2+25−2−254-82−252+25-440000−2+25−2−251−51+500−1+5−1−52−252+251−51+5−1+5−1−500000000000000000000000000000000000000000000000000
χ768-8-480−2−25−2+25-842+252−25-4400001+51−5−2−25−2+25002+252−25−1−5−1+51+51−5−1−5−1+500000000000000000000000000000000000000000000000000
χ778-8-480−2+25−2−25-842−252+25-4400001−51+5−2+25−2−25002−252+25−1+5−1−51−51+5−1+5−1−500000000000000000000000000000000000000000000000000
χ788-8-4-40−2−25−2+25442+252−252-2006i−6i1+51−51+51−500−1−5−1+5−1−5−1+5−1−52−1+521+521−520000−3ζ22−3ζ38−3ζ62−3ζ1183ζ22+3ζ38+3ζ62+3ζ118−3ζ14−3ζ46−3ζ86−3ζ943ζ14+3ζ46+3ζ86+3ζ94000000000000000000000000000000000000000000
χ798-8-4-40−2−25−2+25442+252−252-200−6i6i1+51−51+51−500−1−5−1+5−1−5−1+5−1−52−1+521+521−5200003ζ22+3ζ38+3ζ62+3ζ118−3ζ22−3ζ38−3ζ62−3ζ1183ζ14+3ζ46+3ζ86+3ζ94−3ζ14−3ζ46−3ζ86−3ζ94000000000000000000000000000000000000000000
χ808-8-4-40−2+25−2−25442−252+252-2006i−6i1−51+51−51+500−1+5−1−5−1+5−1−5−1+52−1−521−521+520000−3ζ14−3ζ46−3ζ86−3ζ943ζ14+3ζ46+3ζ86+3ζ94−3ζ22−3ζ38−3ζ62−3ζ1183ζ22+3ζ38+3ζ62+3ζ118000000000000000000000000000000000000000000
χ818-8-4-40−2+25−2−25442−252+252-200−6i6i1−51+51−51+500−1+5−1−5−1+5−1−5−1+52−1−521−521+5200003ζ14+3ζ46+3ζ86+3ζ94−3ζ14−3ζ46−3ζ86−3ζ943ζ22+3ζ38+3ζ62+3ζ118−3ζ22−3ζ38−3ζ62−3ζ118000000000000000000000000000000000000000000

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