Finite Group Databasebeta

← Group #13085735

Character table — Group #13085735

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222444444444444448888888888888121212121515181820202024242424242424242424242424303030303036363636404040606060180
order12334556610103612121515151520203030303012151530306060606060606060246644884121210101220203030303060606060288121240404040121212624242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-111-1-1-11111111111111-1-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-11111-1-111111-1-1-11111-1-1-1-11-1-111-1-1-1-11111-1-1-1
χ4111111111111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111-11-1-111-1-1-1-1-1-1-1111-1-1-1-111111-1-111-1-1-1-1-1-1-11-1-11
χ611111111111111111111111111111111111111-11-1-1-1-1-1-1111-1-1111-1-1-1-11111-111-1-1-1-1-1-1111-111-1
χ711111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111-1
χ811111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11
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+5222220022000−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000−1−52−1−52−1+52−1+520000000
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+522-22200-2-2000−1−52−1+52-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52000001+521+521−521−520000000
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+52-22-2-200-2-20001+521−522−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000001+521+521−521−520000000
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+52-2-2-2-200220001+521−52-21+521−521+521+521−521−521+521+521−521−5200000−1−52−1−52−1+52−1+520000000
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+52−1−52−1−5222220022000−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000−1+52−1+52−1−52−1−520000000
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+52−1−52−1−522-22200-2-2000−1+52−1−52-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52000001−521−521+521+520000000
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+52−1−52−1−52-22-2-200-2-20001−521+522−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000001−521−521+521+520000000
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+52−1−52−1−52-2-2-2-200220001−521+52-21−521+521−521−521+521+521−521−521+521+5200000−1+52−1+52−1−52−1−520000000
χ172222-222222222-2-22222-2-22222-22222-2-2-2-2-2-2-2-2000022000000000000000000-200220000000-2000
χ182222-222222222-2-22222-2-22222-22222-2-2-2-2-2-2-2-20000-2-2000000000000000000200-2-200000002000
χ19222-12222-122-1-1-1222-1-122-1-122-1-1-1-1-1-1-122-1-1-1-120-1-122002-1-122000-1-1-1-10000200-1-100002-1-1-1000
χ20222-12222-122-1-1-1222-1-122-1-122-1-1-1-1-1-1-122-1-1-1-120-1-1-2-200-21122000-1-1-1-10000-200110000-2111000
χ21222-12222-122-1-1-1222-1-122-1-122-1-1-1-1-1-1-122-1-1-1-1-20112200-211-2-200011110000200-1-10000-211-1000
χ22222-12222-122-1-1-1222-1-122-1-122-1-1-1-1-1-1-122-1-1-1-1-2011-2-2002-1-1-2-200011110000-2001100002-1-11000
χ23222-1-2222-122-1-11-222-1-1-2-2-1-1221-1-1-1-111-2-2111100−i3i322000−i3i300000−i3i3−i3i30000-200-1-100000−i3i31000
χ24222-1-2222-122-1-11-222-1-1-2-2-1-1221-1-1-1-111-2-2111100−i3i3-2-2000i3−i300000−i3i3−i3i300002001100000i3−i3-1000
χ25222-1-2222-122-1-11-222-1-1-2-2-1-1221-1-1-1-111-2-2111100i3−i322000i3−i300000i3−i3i3−i30000-200-1-100000i3−i31000
χ26222-1-2222-122-1-11-222-1-1-2-2-1-1221-1-1-1-111-2-2111100i3−i3-2-2000−i3i300000i3−i3i3−i300002001100000−i3i3-1000
χ2722-12222-1222-1-12-1-1-1222222-1-1-1-1-1-1-122-1-1-1-1-1-10200000022200-1220000-1-1-1-1022000000-1-1-10-1-10
χ2822-12222-1222-1-12-1-1-1222222-1-1-1-1-1-1-122-1-1-1-1-1-102000000-2-2-200-1220000-1-1-1-10-2-20000001110110
χ2922-12222-1222-1-12-1-1-1222222-1-1-1-1-1-1-122-1-1-1-1-1-10-2000000222001-2-2000011110-2-2000000-1-1-10110
χ3022-12222-1222-1-12-1-1-1222222-1-1-1-1-1-1-122-1-1-1-1-1-10-2000000-2-2-2001-2-2000011110220000001110-1-10
χ312-222022-2-2-2-22-200222200-2-2-2-2022-2-20000000000002i−2i−i2i2000000000000000002−22i−2i−i2i2−i2i200002−20
χ322-222022-2-2-2-22-200222200-2-2-2-2022-2-20000000000002i−2ii2−i200000000000000000−222i−2ii2−i2i2−i20000−220
χ332-222022-2-2-2-22-200222200-2-2-2-2022-2-2000000000000−2i2i−i2i200000000000000000−22−2i2i−i2i2−i2i20000−220
χ342-222022-2-2-2-22-200222200-2-2-2-2022-2-2000000000000−2i2ii2−i2000000000000000002−2−2i2ii2−i2i2−i200002−20
χ354444-4−1−5−1+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+51−51−50000000000000000000000000000000000000000
χ364444-4−1+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+50000000000000000000000000000000000000000
χ37444-24−1−5−1+54-2−1−5−1+5-2-2-24−1−5−1+51+521−52−1−5−1+51+521−52−1−5−1+5-21+521−521+521−521+521−52−1−5−1+51+521+521−521−5240-2-20000000−1−5−1+50001+521+521−521−5200000000000000000000
χ38444-24−1−5−1+54-2−1−5−1+5-2-2-24−1−5−1+51+521−52−1−5−1+51+521−52−1−5−1+5-21+521−521+521−521+521−52−1−5−1+51+521+521−521−52-402200000001+51−5000−1−52−1−52−1+52−1+5200000000000000000000
χ39444-24−1+5−1−54-2−1+5−1−5-2-2-24−1+5−1−51−521+52−1+5−1−51−521+52−1+5−1−5-21−521+521−521+521−521+52−1+5−1−51−521−521+521+5240-2-20000000−1+5−1−50001−521−521+521+5200000000000000000000
χ40444-24−1+5−1−54-2−1+5−1−5-2-2-24−1+5−1−51−521+52−1+5−1−51−521+52−1+5−1−5-21−521+521−521+521−521+52−1+5−1−51−521−521+521+52-402200000001−51+5000−1+52−1+52−1−52−1−5200000000000000000000
χ41444-2-4−1−5−1+54-2−1−5−1+5-2-22-4−1−5−1+51+521−521+51−51+521−52−1−5−1+521+521−521+521−52−1−52−1+521+51−5−1−52−1−52−1+52−1+5200−2i32i3000000000000ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ92ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ11600000000000000000000
χ42444-2-4−1−5−1+54-2−1−5−1+5-2-22-4−1−5−1+51+521−521+51−51+521−52−1−5−1+521+521−521+521−52−1−52−1+521+51−5−1−52−1−52−1+52−1+52002i3−2i3000000000000−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ92−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ11600000000000000000000
χ43444-2-4−1+5−1−54-2−1+5−1−5-2-22-4−1+5−1−51−521+521−51+51−521+52−1+5−1−521−521+521−521+52−1+52−1−521−51+5−1+52−1+52−1−52−1−5200−2i32i3000000000000ζ4−ζ44+ζ76−ζ116−ζ4+ζ44−ζ76+ζ116ζ28+ζ52−ζ68−ζ92−ζ28−ζ52+ζ68+ζ9200000000000000000000
χ44444-2-4−1+5−1−54-2−1+5−1−5-2-22-4−1+5−1−51−521+521−51+51−521+52−1+5−1−521−521+521−521+52−1+52−1−521−51+5−1+52−1+52−1−52−1−52002i3−2i3000000000000−ζ4+ζ44−ζ76+ζ116ζ4−ζ44+ζ76−ζ116−ζ28−ζ52+ζ68+ζ92ζ28+ζ52−ζ68−ζ9200000000000000000000
χ4544-244−1−5−1+5-24−1−5−1+5-2-24-21+521−52−1−5−1+5−1−5−1+5−1−5−1+51+521−52-21+521−521+521−52−1−5−1+51+521−521+521+521−521−520400000000000-2−1−5−1+500001+521+521−521−520000000000000000
χ4644-244−1−5−1+5-24−1−5−1+5-2-24-21+521−52−1−5−1+5−1−5−1+5−1−5−1+51+521−52-21+521−521+521−52−1−5−1+51+521−521+521+521−521−520-40000000000021+51−50000−1−52−1−52−1+52−1+520000000000000000
χ4744-244−1+5−1−5-24−1+5−1−5-2-24-21−521+52−1+5−1−5−1+5−1−5−1+5−1−51−521+52-21−521+521−521+52−1+5−1−51−521+521−521−521+521+520400000000000-2−1+5−1−500001−521−521+521+520000000000000000
χ4844-244−1+5−1−5-24−1+5−1−5-2-24-21−521+52−1+5−1−5−1+5−1−5−1+5−1−51−521+52-21−521+521−521+52−1+5−1−51−521+521−521−521+521+520-40000000000021−51+50000−1+52−1+52−1−52−1−520000000000000000
χ4944-24-444-2444-2-2-42-2-244-4-444-2-22-2-2-2-2-4-42222220000000000000000000000000000000000000000
χ5044-24-4−1−5−1+5-24−1−5−1+5-2-2-421+521−52−1−5−1+51+51−5−1−5−1+51+521−5221+521−521+521−521+51−5−1−52−1+52−1−52−1−52−1+52−1+5200000000000000000000ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ1160000000000000000
χ5144-24-4−1−5−1+5-24−1−5−1+5-2-2-421+521−52−1−5−1+51+51−5−1−5−1+51+521−5221+521−521+521−521+51−5−1−52−1+52−1−52−1−52−1+52−1+5200000000000000000000−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ1160000000000000000
χ5244-24-4−1+5−1−5-24−1+5−1−5-2-2-421−521+52−1+5−1−51−51+5−1+5−1−51−521+5221−521+521−521+521−51+5−1+52−1−52−1+52−1+52−1−52−1−5200000000000000000000−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ920000000000000000
χ5344-24-4−1+5−1−5-24−1+5−1−5-2-2-421−521+52−1+5−1−51−51+5−1+5−1−51−521+5221−521+521−521+521−51+5−1+52−1−52−1+52−1+52−1−52−1−5200000000000000000000ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ920000000000000000
χ5444-2-2444-2-24411-2-2-2-2-2-244-2-2-2-211111-2-2-2-21111000000004-2-20000000000000000000000-2110000
χ5544-2-2444-2-24411-2-2-2-2-2-244-2-2-2-211111-2-2-2-2111100000000-42200000000000000000000002-1-10000
χ5644-2-2-444-2-2441122-2-2-2-2-4-4-2-2-2-2-111112222-1-1-1-1000000000−2i32i300000000000000000000000i3−i30000
χ5744-2-2-444-2-2441122-2-2-2-2-4-4-2-2-2-2-111112222-1-1-1-10000000002i3−2i300000000000000000000000−i3i30000
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+51−500000000000000−2i22i2000000000000000000000ζ7+ζ13+ζ23+ζ37+ζ47+ζ53+ζ77+ζ103−ζ7−ζ13−ζ23−ζ37−ζ47−ζ53−ζ77−ζ103ζ29+ζ31+ζ61+ζ71+ζ79+ζ101+ζ109+ζ119−ζ29−ζ31−ζ61−ζ71−ζ79−ζ101−ζ109−ζ1190000000
χ594-4440−1−5−1+5-4-41+51−54-400−1−5−1+5−1−5−1+5001+51−51+51−50−1−5−1+51+51−5000000000000002i2−2i2000000000000000000000−ζ7−ζ13−ζ23−ζ37−ζ47−ζ53−ζ77−ζ103ζ7+ζ13+ζ23+ζ37+ζ47+ζ53+ζ77+ζ103−ζ29−ζ31−ζ61−ζ71−ζ79−ζ101−ζ109−ζ119ζ29+ζ31+ζ61+ζ71+ζ79+ζ101+ζ109+ζ1190000000
χ604-4440−1+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+500000000000000−2i22i2000000000000000000000ζ29+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
χ614-4440−1+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+5000000000000002i2−2i2000000000000000000000−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
χ624-44-2044-42-4-4-220044-2-20022-4-40-2-2220000000000004i−4i000000000000000000000−2i2i00000000000
χ634-44-2044-42-4-4-220044-2-20022-4-40-2-222000000000000−4i4i0000000000000000000002i−2i00000000000
χ644-4-240442-4-4-4-2200-2-24400-4-4220-2-22200000000000000000000000000000000022−220000000000−220
χ654-4-240442-4-4-4-2200-2-24400-4-4220-2-222000000000000000000000000000000000−222200000000002−20
χ6688-4-48−2−25−2+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+520000000000000000000000000000000000000000
χ6788-4-48−2+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+52−1−52−1−520000000000000000000000000000000000000000
χ6888-4-4-8−2−25−2+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+521−521−520000000000000000000000000000000000000000
χ6988-4-4-8−2+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+520000000000000000000000000000000000000000
χ708-88-40−2−25−2+25-842+252−25-4400−2−25−2+251+51−500−1−5−1+52+252−2501+51−5−1−5−1+5000000000000000000000000000000000000000000000000
χ718-88-40−2+25−2−25-842−252+25-4400−2+25−2−251−51+500−1+5−1−52−252+2501−51+5−1+5−1−5000000000000000000000000000000000000000000000000
χ728-8-480−2−25−2+254-82+252−25-44001+51−5−2−25−2+25002+252−25−1−5−1+501+51−5−1−5−1+5000000000000000000000000000000000000000000000000
χ738-8-480−2+25−2−254-82−252+25-44001−51+5−2+25−2−25002−252+25−1+5−1−501−51+5−1+5−1−5000000000000000000000000000000000000000000000000
χ748-8-4-408844-8-82-200-4-4-4-4004444022-2-2000000000000000000000000000000000000000000000000
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+521−520000−3ζ22+3ζ38−3ζ62+3ζ1183ζ22−3ζ38+3ζ62−3ζ1183ζ14−3ζ46−3ζ86+3ζ94−3ζ14+3ζ46+3ζ86−3ζ940000000000000000000000000000000000000000
χ768-8-4-40−2−25−2+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+3ζ940000000000000000000000000000000000000000
χ778-8-4-40−2+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+3ζ1180000000000000000000000000000000000000000
χ788-8-4-40−2+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+3ζ62−3ζ1180000000000000000000000000000000000000000

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