Finite Group Databasebeta

← Group #13085803

Character table — Group #13085803

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222222222444444444444444488888888888812122020202020202020202424242424242424242424242424363636363660609090120120
order12334556610103612121212151515152020303030301515303060606060606060602282424242424242424661010101030303030303030308404040402424612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-11111111111-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-11
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-1-11-1111-1
χ5111111111111111111111111111111111111111-11111111111-11-1-111-1-1-1-11111-1-1-1-1-11-1-1-11-1
χ6111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1111-11
χ7111111111111111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111
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+522200000000022−1−52−1+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+52000000
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+522-20000000002-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52-21+521+521−521−52000000
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+52-22000000000-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-21+521+521−521−52000000
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+52-2-2000000000-2-21+521−521+521−521+521+521−521−521+521+521−521−522−1−52−1−52−1+52−1+52000000
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+52−1−52−1−522200000000022−1+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+52−1−52−1−52000000
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+52−1−52−1−522-20000000002-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52-21−521−521+521+52000000
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+52−1−52−1−52-22000000000-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-21−521−521+521+52000000
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+52−1−52−1−52-2-2000000000-2-21−521+521−521+521−521−521+521+521−521−521+521+522−1+52−1+52−1−52−1−52000000
χ172222-222222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000002-200
χ182222-222222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-2200
χ19222-1222-1222-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-102222-1-1-1-1-1-10-100220000-1-1-1-1000002000-10
χ20222-1222-1222-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-102-2-2-21111110-100220000-1-1-1-100000-200010
χ21222-1222-1222-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-10-2222-1-1-1-1-1-10100-2-20000111100000-200010
χ22222-1222-1222-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-10-2-2-2-21111110100-2-200001111000002000-10
χ2322-122222-122-1-12-1-1-1-12-1222-12-12-1-1-1-1-12-12-1-1-1-1202-1-122-1-1-1-1-102200-1-1-1-100000000002000-1
χ2422-122222-122-1-12-1-1-1-12-1222-12-12-1-1-1-1-12-12-1-1-1-120-211-2-21111-102200-1-1-1-10000000000-20001
χ2522-122222-122-1-12-1-1-1-12-1222-12-12-1-1-1-1-12-12-1-1-1-1-202-1-122-1-1-1-110-2-20011110000000000-20001
χ2622-122222-122-1-12-1-1-1-12-1222-12-12-1-1-1-1-12-12-1-1-1-1-20-211-2-2111110-2-200111100000000002000-1
χ274444-4−1−5−1+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+51−51−5000000000000000000000000000000000000
χ284444-4−1+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+5000000000000000000000000000000000000
χ29444-24−1−5−1+5-24−1−5−1+5-2-2-24-2-2−1−51+52−1+51−52−1−5−1+5−1−51+52−1+51−521+521−521+521−52−1−51+52−1+51−521+521+521−521−52040000000000-200−1−5−1+500001+521+521−521−5200000000000
χ30444-24−1−5−1+5-24−1−5−1+5-2-2-24-2-2−1−51+52−1+51−52−1−5−1+5−1−51+52−1+51−521+521−521+521−52−1−51+52−1+51−521+521+521−521−520-400000000002001+51−50000−1−52−1−52−1+52−1+5200000000000
χ31444-24−1+5−1−5-24−1+5−1−5-2-2-24-2-2−1+51−52−1−51+52−1+5−1−5−1+51−52−1−51+521−521+521−521+52−1+51−52−1−51+521−521−521+521+52040000000000-200−1+5−1−500001−521−521+521+5200000000000
χ32444-24−1+5−1−5-24−1+5−1−5-2-2-24-2-2−1+51−52−1−51+52−1+5−1−5−1+51−52−1−51+521−521+521−521+52−1+51−52−1−51+521−521−521+521+520-400000000002001−51+50000−1+52−1+52−1−52−1−5200000000000
χ33444-2-444-2444-2-22-4224-24-2-4-44-24-2-2-2-2-2-42-422222000000000000000000000000000000000000
χ34444-2-4−1−5−1+5-24−1−5−1+5-2-22-422−1−51+52−1+51−521+51−5−1−51+52−1+51−521+521−521+521−521+5−1−521−5−1+52−1−52−1−52−1+52−1+52000000000000000000000ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ11600000000000
χ35444-2-4−1−5−1+5-24−1−5−1+5-2-22-422−1−51+52−1+51−521+51−5−1−51+52−1+51−521+521−521+521−521+5−1−521−5−1+52−1−52−1−52−1+52−1+52000000000000000000000−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ11600000000000
χ36444-2-4−1+5−1−5-24−1+5−1−5-2-22-422−1+51−52−1−51+521−51+5−1+51−52−1−51+521−521+521−521+521−5−1+521+5−1−52−1+52−1+52−1−52−1−52000000000000000000000−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ9200000000000
χ37444-2-4−1+5−1−5-24−1+5−1−5-2-22-422−1+51−52−1−51+521−51+5−1+51−52−1−51+521−521+521−521+521−5−1+521+5−1−52−1+52−1+52−1−52−1−52000000000000000000000ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ9200000000000
χ3844-244−1−5−1+54-2−1−5−1+5-2-24-2-2-21+52−1−51−52−1+5−1−5−1+51+52−1−51−52−1+51+521−521+521−521+52−1−51−52−1+51+521+521−521−5240000000000-20−1−5−1+5001+521+521−521−52000000000000000
χ3944-244−1−5−1+54-2−1−5−1+5-2-24-2-2-21+52−1−51−52−1+5−1−5−1+51+52−1−51−52−1+51+521−521+521−521+52−1−51−52−1+51+521+521−521−52-40000000000201+51−500−1−52−1−52−1+52−1+52000000000000000
χ4044-244−1+5−1−54-2−1+5−1−5-2-24-2-2-21−52−1+51+52−1−5−1+5−1−51−52−1+51+52−1−51−521+521−521+521−52−1+51+52−1−51−521−521+521+5240000000000-20−1+5−1−5001−521−521+521+52000000000000000
χ4144-244−1+5−1−54-2−1+5−1−5-2-24-2-2-21−52−1+51+52−1−5−1+5−1−51−52−1+51+52−1−51−521+521−521+521−52−1+51+52−1−51−521−521+521+52-40000000000201−51+500−1+52−1+52−1−52−1−52000000000000000
χ4244-24-4444-244-2-2-4222-24-24-4-4-24-24-2-2-2-22-42-42222000000000000000000000000000000000000
χ4344-24-4−1−5−1+54-2−1−5−1+5-2-2-42221+52−1−51−52−1+51+51−51+52−1−51−52−1+51+521−521+521−52−1−521+5−1+521−5−1−52−1−52−1+52−1+5200000000000000000ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116000000000000000
χ4444-24-4−1−5−1+54-2−1−5−1+5-2-2-42221+52−1−51−52−1+51+51−51+52−1−51−52−1+51+521−521+521−52−1−521+5−1+521−5−1−52−1−52−1+52−1+5200000000000000000−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116000000000000000
χ4544-24-4−1+5−1−54-2−1+5−1−5-2-2-42221−52−1+51+52−1−51−51+51−52−1+51+52−1−51−521+521−521+52−1+521−5−1−521+5−1+52−1+52−1−52−1−5200000000000000000−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92000000000000000
χ4644-24-4−1+5−1−54-2−1+5−1−5-2-2-42221−52−1+51+52−1−51−51+51−52−1+51+52−1−51−521+521−521+52−1+521−5−1−521+5−1+52−1+52−1−52−1−5200000000000000000ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92000000000000000
χ4744-2-2444-2-24411-2-211-2-2-2-244-2-2-2-21111-2-2-2-21111004-2-2-2-211110000000000000000000000000
χ4844-2-2444-2-24411-2-211-2-2-2-244-2-2-2-21111-2-2-2-2111100-42222-1-1-1-10000000000000000000000000
χ4944-2-2-444-2-2441122-1-1-2-2-2-2-4-4-2-2-2-211112222-1-1-1-100000003i3i−3i−3i0000000000000000000000000
χ5044-2-2-444-2-2441122-1-1-2-2-2-2-4-4-2-2-2-211112222-1-1-1-10000000−3i−3i3i3i0000000000000000000000000
χ514-444044-4-4-4-44-40000444400-4-4-4-444-4-400000000000000000000000000000000000000000000
χ524-4440−1−5−1+5-4-41+51−54-40000−1−5−1−5−1+5−1+5001+51+51−51−5−1−5−1+51+51−50000000000000000000000000000000000−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+ζ119000000
χ534-4440−1−5−1+5-4-41+51−54-40000−1−5−1−5−1+5−1+5001+51+51−51−5−1−5−1+51+51−50000000000000000000000000000000000ζ7+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−ζ119000000
χ544-4440−1+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+50000000000000000000000000000000000ζ29+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+ζ103000000
χ554-4440−1+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+50000000000000000000000000000000000−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−ζ103000000
χ564-44-20442-4-4-4-2200004-24-200-42-42-2-2220000000000000−i6i6−i6i6−i6i60000000000000000000000000
χ574-44-20442-4-4-4-2200004-24-200-42-42-2-2220000000000000i6−i6i6−i6i6−i60000000000000000000000000
χ584-4-24044-42-4-4-220000-24-24002-42-4-2-222000000000006−6006−6−660000000000000000000000000
χ594-4-24044-42-4-4-220000-24-24002-42-4-2-22200000000000−6600−666−60000000000000000000000000
χ604-4-2-204422-4-41-1003i−3i-2-2-2-200222211-1-100003i−3i3i−3i0006−6−i6i6−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ1090000000000000000000000000
χ614-4-2-204422-4-41-1003i−3i-2-2-2-200222211-1-100003i−3i3i−3i000−66i6−i6ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ1090000000000000000000000000
χ624-4-2-204422-4-41-100−3i3i-2-2-2-200222211-1-10000−3i3i−3i3i0006−6i6−i6−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ1190000000000000000000000000
χ634-4-2-204422-4-41-100−3i3i-2-2-2-200222211-1-10000−3i3i−3i3i000−66−i6i6ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ1190000000000000000000000000
χ6488-4-48−2−25−2+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+52000000000000000000000000000000000000
χ6588-4-48−2+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+52−1−52−1−52000000000000000000000000000000000000
χ6688-4-4-8−2−25−2+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+521−521−52000000000000000000000000000000000000
χ6788-4-4-8−2+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+52000000000000000000000000000000000000
χ688-88-40−2−25−2+254-82+252−25-440000−2−251+5−2+251−5002+25−1−52−25−1+51+51−5−1−5−1+500000000000000000000000000000000000000000000
χ698-88-40−2+25−2−254-82−252+25-440000−2+251−5−2−251+5002−25−1+52+25−1−51−51+5−1+5−1−500000000000000000000000000000000000000000000
χ708-8-480−2−25−2+25-842+252−25-4400001+5−2−251−5−2+2500−1−52+25−1+52−251+51−5−1−5−1+500000000000000000000000000000000000000000000
χ718-8-480−2+25−2−25-842−252+25-4400001−5−2+251+5−2−2500−1+52−25−1−52+251−51+5−1+5−1−500000000000000000000000000000000000000000000
χ728-8-4-40−2−25−2+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+3ζ94000000000000000000000000000000000000
χ738-8-4-40−2−25−2+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+3ζ94−3ζ14−3ζ46−3ζ86−3ζ94000000000000000000000000000000000000
χ748-8-4-40−2+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+3ζ118000000000000000000000000000000000000
χ758-8-4-40−2+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+3ζ118−3ζ22−3ζ38−3ζ62−3ζ118000000000000000000000000000000000000

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