Finite Group Databasebeta

← Group #13085778

Character table — Group #13085778

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222222222444444444444448888888888888121212122020202424242424242424242424242430303030363636363640404060606060180
order1233455661010361212151515152020303030301215153030606060606060606022664121261010101030303030303030302412128404040401212126824242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-111111-111-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111-11-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1111-1
χ611111111111111111111111111111111111111-11-1-1-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-11
χ711111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ922222−1−52−1+5222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222220002−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200002−1−52−1−52−1+52−1+5200000000
χ1022222−1−52−1+5222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-222000-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000-21+521+521−521−5200000000
χ1122222−1−52−1+5222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-22-2-200021+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000-21+521+521−521−5200000000
χ1222222−1−52−1+5222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2000-21+521−521+521−521+521+521−521−521+521+521−521−5200002−1−52−1−52−1+52−1+5200000000
χ1322222−1+52−1−5222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222220002−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200002−1+52−1+52−1−52−1−5200000000
χ1422222−1+52−1−5222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-222000-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000-21−521−521+521+5200000000
χ1522222−1+52−1−5222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-2-200021−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000-21−521−521+521+5200000000
χ1622222−1+52−1−5222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2000-21−521+521−521+521−521−521+521+521−521−521+521+5200002−1+52−1+52−1−52−1−5200000000
χ172222-222222222-2-22222-2-22222-22222-2-2-2-2-2-2-2-2000000000000000000002-2-2-20000000020000
χ182222-222222222-2-22222-2-22222-22222-2-2-2-2-2-2-2-200000000000000000000-222200000000-20000
χ19222-12222-122-1-1-122-12-1222-12-1-1-1-1-1-12-12-1-1-1-1-120-1-12-1-102200-1-1-1-1000022-1-1000002-1-1-10000
χ20222-12222-122-1-1-122-12-1222-12-1-1-1-1-1-12-12-1-1-1-1-120-1-1-21102200-1-1-1-10000-2-21100000-21110000
χ21222-12222-122-1-1-122-12-1222-12-1-1-1-1-1-12-12-1-1-1-1-1-20112-1-10-2-20011110000-2-211000002-1-110000
χ22222-12222-122-1-1-122-12-1222-12-1-1-1-1-1-12-12-1-1-1-1-1-2011-2110-2-2001111000022-1-100000-211-10000
χ23222-1-2222-122-1-11-22-12-1-2-22-12-11-1-1-1-1-21-21111100−i3i30−i3i300000−i3i3−i3i300002-211000000−i3i3-10000
χ24222-1-2222-122-1-11-22-12-1-2-22-12-11-1-1-1-1-21-21111100−i3i30i3−i300000−i3i3−i3i30000-22-1-1000000i3−i310000
χ25222-1-2222-122-1-11-22-12-1-2-22-12-11-1-1-1-1-21-21111100i3−i30−i3i300000i3−i3i3−i30000-22-1-1000000−i3i310000
χ26222-1-2222-122-1-11-22-12-1-2-22-12-11-1-1-1-1-21-21111100i3−i30i3−i300000i3−i3i3−i300002-211000000i3−i3-10000
χ2722-12222-1222-1-12-1-12-1222-12-12-1-1-1-1-1-12-12-1-1-1-10200222-100220000-1-1-1-1000000000-1-1-102-1-10
χ2822-12222-1222-1-12-1-12-1222-12-12-1-1-1-1-1-12-12-1-1-1-10200-2-2-2-100220000-1-1-1-10000000001110-2110
χ2922-12222-1222-1-12-1-12-1222-12-12-1-1-1-1-1-12-12-1-1-1-10-200222100-2-200001111000000000-1-1-10-2110
χ3022-12222-1222-1-12-1-12-1222-12-12-1-1-1-1-1-12-12-1-1-1-10-200-2-2-2100-2-20000111100000000011102-1-10
χ314444-4−1−5−1+544−1−5−1+544-4-4−1−5−1−5−1+5−1+51+51−5−1−5−1−5−1+5−1+5-4−1−5−1+5−1−5−1+51+51+51−51−51+51+51−51−50000000000000000000000000000000000000
χ324444-4−1+5−1−544−1+5−1−544-4-4−1+5−1+5−1−5−1−51−51+5−1+5−1+5−1−5−1−5-4−1+5−1−5−1+5−1−51−51−51+51+51−51−51+51+50000000000000000000000000000000000000
χ33444-24−1−5−1+54-2−1−5−1+5-2-2-24−1−51+52−1+51−52−1−5−1+5−1−51+52−1+51−52-21+521−521+521−52−1−51+52−1+51−521+521+521−521−5240-2-20000−1−5−1+5001+521+521−521−52000000000000000000000
χ34444-24−1−5−1+54-2−1−5−1+5-2-2-24−1−51+52−1+51−52−1−5−1+5−1−51+52−1+51−52-21+521−521+521−52−1−51+52−1+51−521+521+521−521−52-402200001+51−500−1−52−1−52−1+52−1+52000000000000000000000
χ35444-24−1+5−1−54-2−1+5−1−5-2-2-24−1+51−52−1−51+52−1+5−1−5−1+51−52−1−51+52-21−521+521−521+52−1+51−52−1−51+521−521−521+521+5240-2-20000−1+5−1−5001−521−521+521+52000000000000000000000
χ36444-24−1+5−1−54-2−1+5−1−5-2-2-24−1+51−52−1−51+52−1+5−1−5−1+51−52−1−51+52-21−521+521−521+52−1+51−52−1−51+521−521−521+521+52-402200001−51+500−1+52−1+52−1−52−1−52000000000000000000000
χ37444-2-4−1−5−1+54-2−1−5−1+5-2-22-4−1−51+52−1+51−521+51−5−1−51+52−1+51−5221+521−521+521−521+5−1−521−5−1+52−1−52−1−52−1+52−1+5200−2i32i300000000ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116000000000000000000000
χ38444-2-4−1−5−1+54-2−1−5−1+5-2-22-4−1−51+52−1+51−521+51−5−1−51+52−1+51−5221+521−521+521−521+5−1−521−5−1+52−1−52−1−52−1+52−1+52002i3−2i300000000−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116000000000000000000000
χ39444-2-4−1+5−1−54-2−1+5−1−5-2-22-4−1+51−52−1−51+521−51+5−1+51−52−1−51+5221−521+521−521+521−5−1+521+5−1−52−1+52−1+52−1−52−1−5200−2i32i300000000ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92000000000000000000000
χ40444-2-4−1+5−1−54-2−1+5−1−5-2-22-4−1+51−52−1−51+521−51+5−1+51−52−1−51+5221−521+521−521+521−5−1+521+5−1−52−1+52−1+52−1−52−1−52002i3−2i300000000−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92000000000000000000000
χ4144-244−1−5−1+5-24−1−5−1+5-2-24-21+52−1−51−52−1+5−1−5−1+51+52−1−51−52−1+5-21+521−521+521−521+52−1−51−52−1+51+521+521−521−520400000-200−1−5−1+500001+521+521−521−5200000000000000000
χ4244-244−1−5−1+5-24−1−5−1+5-2-24-21+52−1−51−52−1+5−1−5−1+51+52−1−51−52−1+5-21+521−521+521−521+52−1−51−52−1+51+521+521−521−520-4000002001+51−50000−1−52−1−52−1+52−1+5200000000000000000
χ4344-244−1+5−1−5-24−1+5−1−5-2-24-21−52−1+51+52−1−5−1+5−1−51−52−1+51+52−1−5-21−521+521−521+521−52−1+51+52−1−51−521−521+521+520400000-200−1+5−1−500001−521−521+521+5200000000000000000
χ4444-244−1+5−1−5-24−1+5−1−5-2-24-21−52−1+51+52−1−5−1+5−1−51−52−1+51+52−1−5-21−521+521−521+521−52−1+51+52−1−51−521−521+521+520-4000002001−51+50000−1+52−1+52−1−52−1−5200000000000000000
χ4544-24-444-2444-2-2-42-24-24-4-4-24-242-2-2-2-22-42-422220000000000000000000000000000000000000
χ4644-24-4−1−5−1+5-24−1−5−1+5-2-2-421+52−1−51−52−1+51+51−51+52−1−51−52−1+521+521−521+521−52−1−521+5−1+521−5−1−52−1−52−1+52−1+520000000000000000ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ11600000000000000000
χ4744-24-4−1−5−1+5-24−1−5−1+5-2-2-421+52−1−51−52−1+51+51−51+52−1−51−52−1+521+521−521+521−52−1−521+5−1+521−5−1−52−1−52−1+52−1+520000000000000000−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ11600000000000000000
χ4844-24-4−1+5−1−5-24−1+5−1−5-2-2-421−52−1+51+52−1−51−51+51−52−1+51+52−1−521−521+521−521+52−1+521−5−1−521+5−1+52−1+52−1−52−1−520000000000000000−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ9200000000000000000
χ4944-24-4−1+5−1−5-24−1+5−1−5-2-2-421−52−1+51+52−1−51−51+51−52−1+51+52−1−521−521+521−521+52−1+521−5−1−521+5−1+52−1+52−1−52−1−520000000000000000ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ9200000000000000000
χ5044-2-2444-2-24411-2-2-2-2-2-244-2-2-2-211111-2-2-2-2111100004-2-20000000000000000000000-21100000
χ5144-2-2444-2-24411-2-2-2-2-2-244-2-2-2-211111-2-2-2-211110000-42200000000000000000000002-1-100000
χ5244-2-2-444-2-2441122-2-2-2-2-4-4-2-2-2-2-111112222-1-1-1-100000−2i32i300000000000000000000000i3−i300000
χ5344-2-2-444-2-2441122-2-2-2-2-4-4-2-2-2-2-111112222-1-1-1-1000002i3−2i300000000000000000000000−i3i300000
χ544-444044-4-4-4-44-400444400-4-4-4-4044-4-4000000000000000000000000000000000000000000000
χ554-4440−1−5−1+5-4-41+51−54-400−1−5−1−5−1+5−1+5001+51+51−51−50−1−5−1+51+51−5000000000000000000000000000000000−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+ζ11900000000
χ564-4440−1−5−1+5-4-41+51−54-400−1−5−1−5−1+5−1+5001+51+51−51−50−1−5−1+51+51−5000000000000000000000000000000000ζ7+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−ζ11900000000
χ574-4440−1+5−1−5-4-41−51+54-400−1+5−1+5−1−5−1−5001−51−51+51+50−1+5−1−51−51+5000000000000000000000000000000000ζ29+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+ζ10300000000
χ584-4440−1+5−1−5-4-41−51+54-400−1+5−1+5−1−5−1−5001−51−51+51+50−1+5−1−51−51+5000000000000000000000000000000000−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−ζ10300000000
χ594-44-2044-42-4-4-22004-24-200-42-420-2-22200000000000000000000000000000023−230000000000000
χ604-44-2044-42-4-4-22004-24-200-42-420-2-222000000000000000000000000000000−23230000000000000
χ614-4-240442-4-4-4-2200-24-24002-42-40-2-2220000000000000000000000000000000000000000006−60
χ624-4-240442-4-4-4-2200-24-24002-42-40-2-222000000000000000000000000000000000000000000−660
χ6388-4-48−2−25−2+25-4-4−2−25−2+2522-4-41+51+51−51−5−2−25−2+251+51+51−51−52−1−52−1+52−1−52−1+521+51+51−51−5−1−52−1−52−1+52−1+520000000000000000000000000000000000000
χ6488-4-48−2+25−2−25-4-4−2+25−2−2522-4-41−51−51+51+5−2+25−2−251−51−51+51+52−1+52−1−52−1+52−1−521−51−51+51+5−1+52−1+52−1−52−1−520000000000000000000000000000000000000
χ6588-4-4-8−2−25−2+25-4-4−2−25−2+2522441+51+51−51−52+252−251+51+51−51−5-2−1−52−1+52−1−52−1+52−1−5−1−5−1+5−1+51+521+521−521−520000000000000000000000000000000000000
χ6688-4-4-8−2+25−2−25-4-4−2+25−2−2522441−51−51+51+52−252+251−51−51+51+5-2−1+52−1−52−1+52−1−52−1+5−1+5−1−5−1−51−521−521+521+520000000000000000000000000000000000000
χ678-88-40−2−25−2+25-842+252−25-4400−2−251+5−2+251−5002+25−1−52−25−1+501+51−5−1−5−1+5000000000000000000000000000000000000000000000
χ688-88-40−2+25−2−25-842−252+25-4400−2+251−5−2−251+5002−25−1+52+25−1−501−51+5−1+5−1−5000000000000000000000000000000000000000000000
χ698-8-480−2−25−2+254-82+252−25-44001+5−2−251−5−2+2500−1−52+25−1+52−2501+51−5−1−5−1+5000000000000000000000000000000000000000000000
χ708-8-480−2+25−2−254-82−252+25-44001−5−2+251+5−2−2500−1+52−25−1−52+2501−51+5−1+5−1−5000000000000000000000000000000000000000000000
χ718-8-4-408844-8-82-200-4-4-4-4004444022-2-2000000000000000000000000000000000000000000000
χ728-8-4-40−2−25−2+25442+252−252-2001+51+51−51−500−1−5−1−5−1+5−1+50−1−52−1+521+521−520000−3ζ22+3ζ38−3ζ62+3ζ1183ζ22−3ζ38+3ζ62−3ζ1183ζ14−3ζ46−3ζ86+3ζ94−3ζ14+3ζ46+3ζ86−3ζ940000000000000000000000000000000000000
χ738-8-4-40−2−25−2+25442+252−252-2001+51+51−51−500−1−5−1−5−1+5−1+50−1−52−1+521+521−5200003ζ22−3ζ38+3ζ62−3ζ118−3ζ22+3ζ38−3ζ62+3ζ118−3ζ14+3ζ46+3ζ86−3ζ943ζ14−3ζ46−3ζ86+3ζ940000000000000000000000000000000000000
χ748-8-4-40−2+25−2−25442−252+252-2001−51−51+51+500−1+5−1+5−1−5−1−50−1+52−1−521−521+5200003ζ14−3ζ46−3ζ86+3ζ94−3ζ14+3ζ46+3ζ86−3ζ943ζ22−3ζ38+3ζ62−3ζ118−3ζ22+3ζ38−3ζ62+3ζ1180000000000000000000000000000000000000
χ758-8-4-40−2+25−2−25442−252+252-2001−51−51+51+500−1+5−1+5−1−5−1−50−1+52−1−521−521+520000−3ζ14+3ζ46+3ζ86−3ζ943ζ14−3ζ46−3ζ86+3ζ94−3ζ22+3ζ38−3ζ62+3ζ1183ζ22−3ζ38+3ζ62−3ζ1180000000000000000000000000000000000000

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