Finite Group Databasebeta

← Group #14513324

Character table — Group #14513324

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size11222223344466666888810101212121212121216161616162024242424242424242424242430303030303032323232323232484848486060608080120120160
order12455101022420204101010103620208848888202012151530302442020404040404040404044448812606060606060202020202242424246
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-111-1-11
χ3111111111111111111111-1-1111111111111-1111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-11-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-111-1-111-1
χ5111111111-1111111111-1-111-111111111111-1-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1
χ6111111111-1111111111-1-111-1-1-1-1-11111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-11111-1
χ7111111111-1111111111-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111
χ8111111111-1111111111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111111-1-1-1-11
χ922222222222222222-1-122222000022-1-1-1-1-12002200000000000022-1-1-1-1-1-1-10000200-1-100-1
χ1022222222222222222-1-122-2-22000022-1-1-1-1-1-20022000000000000-2-2-1-1-1-1-1-1-10000-20011001
χ11222222222-22222222-1-1-2-222-2000022-1-1-1-1-1-200-2-2000000000000221-1-111110000-200-1-1001
χ12222222222-22222222-1-1-2-2-2-2-2000022-1-1-1-1-1200-2-2000000000000-2-21-1-1111100002001100-1
χ13222−1−52−1+52−1−52−1+52222−1−52−1+522−1−52−1+52−1−52−1+5222−1−52−1+520022222−1−52−1+522−1−52−1+52−1−52−1+52022−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000002−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5200000000
χ14222−1−52−1+52−1−52−1+52222−1−52−1+522−1−52−1+52−1−52−1+5222−1−52−1+52002-2-2-2-2−1−52−1+522−1−52−1+52−1−52−1+520-2-2−1−52−1+521+521+521−521−521+521+521−521−520000002−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−5200000000
χ15222−1−52−1+52−1−52−1+5222-2−1−52−1+522−1−52−1+52−1−52−1+52221+521−5200-22222−1−52−1+522−1−52−1+52−1−52−1+520-2-21+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000-2−1−52−1+521+521+521−521−521+521−521+521−5200000000
χ16222−1−52−1+52−1−52−1+5222-2−1−52−1+522−1−52−1+52−1−52−1+52221+521−5200-2-2-2-2-2−1−52−1+522−1−52−1+52−1−52−1+520221+521−521+521+521−521−521+521+521−521−52000000-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+5200000000
χ17222−1+52−1−52−1+52−1−52222−1+52−1−522−1+52−1−52−1+52−1−5222−1+52−1−520022222−1+52−1−522−1+52−1−52−1+52−1−52022−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000002−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5200000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−522−1+52−1−52−1+52−1−5222−1+52−1−52002-2-2-2-2−1+52−1−522−1+52−1−52−1+52−1−520-2-2−1+52−1−521−521−521+521+521−521−521+521+520000002−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+5200000000
χ19222−1+52−1−52−1+52−1−5222-2−1+52−1−522−1+52−1−52−1+52−1−52221−521+5200-22222−1+52−1−522−1+52−1−52−1+52−1−520-2-21−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000-2−1+52−1−521−521−521+521+521−521+521−521+5200000000
χ20222−1+52−1−52−1+52−1−5222-2−1+52−1−522−1+52−1−52−1+52−1−52221−521+5200-2-2-2-2-2−1+52−1−522−1+52−1−52−1+52−1−520221−521+521−521−521+521+521−521−521+521+52000000-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−5200000000
χ2122-22222220-2-2-2222222000000000-2-2-2222200000000000002222000-2-2000000000-2-200000
χ2222-22222220-2-2-2222222000000000-2-2-222220000000000000-2-2-2-2000-2-20000000002200000
χ232-2022-2-2-22000022-2-22-200−i2i202−22−200022-2-2000002−22−22−22−22i−2i2i−2i−i2i200000000000000−i2i2000
χ242-2022-2-2-22000022-2-22-200−i2i20−22−2200022-2-200000−22−22−22−22−2i2i−2i2i−i2i200000000000000−i2i2000
χ252-2022-2-2-22000022-2-22-200i2−i202−22−200022-2-2000002−22−22−22−2−2i2i−2i2ii2−i200000000000000i2−i2000
χ262-2022-2-2-22000022-2-22-200i2−i20−22−2200022-2-200000−22−22−22−222i−2i2i−2ii2−i200000000000000i2−i2000
χ273333333-1-1333-1-1-1-1-1003333-111-1-1-1-10000031-1-1-11111-1-1-1-111-1-1-1-1000000011-1-1-11-1001-10
χ283333333-1-1333-1-1-1-1-1003333-1-1-111-1-1000003-11-1-1-1-1-1-11111-1-111-1-10000000-1-111-1-1100-110
χ293333333-1-1333-1-1-1-1-10033-3-3-111-1-1-1-100000-31-1-1-11111-1-1-1-1-1-11111000000011-1-11-1100-110
χ303333333-1-1333-1-1-1-1-10033-3-3-1-1-111-1-100000-3-11-1-1-1-1-1-1111111-1-1110000000-1-11111-1001-10
χ313333333-1-1-333-1-1-1-1-100-3-333111-1-1-1-100000-3-11111111-1-1-1-111-1-1-1-10000000-1-11111-100-110
χ323333333-1-1-333-1-1-1-1-100-3-3331-1-111-1-100000-31-111-1-1-1-11111-1-111-1-1000000011-1-11-11001-10
χ333333333-1-1-333-1-1-1-1-100-3-3-3-3111-1-1-1-1000003-11111111-1-1-1-1-1-111110000000-1-111-1-11001-10
χ343333333-1-1-333-1-1-1-1-100-3-3-3-31-1-111-1-10000031-111-1-1-1-1111111-1-111000000011-1-1-11-100-110
χ35444−1−5−1+5−1−5−1+5444−1−5−1+54−1−5−1+5−1−5−1+5-2-2−1−5−1+50040000−1−5−1+5-21+521−521+521−52000−1−5−1+500000000000000-21+521−521+521+521−521−52000000000000
χ36444−1−5−1+5−1−5−1+544-4−1−5−1+54−1−5−1+5−1−5−1+5-2-21+51−500-40000−1−5−1+5-21+521−521+521−520001+51−50000000000000021+521−52−1−52−1−52−1+52−1+52000000000000
χ37444−1+5−1−5−1+5−1−5444−1+5−1−54−1+5−1−5−1+5−1−5-2-2−1+5−1−50040000−1+5−1−5-21−521+521−521+52000−1+5−1−500000000000000-21−521+521−521−521+521+52000000000000
χ38444−1+5−1−5−1+5−1−544-4−1+5−1−54−1+5−1−5−1+5−1−5-2-21−51+500-40000−1+5−1−5-21−521+521−521+520001−51+50000000000000021−521+52−1+52−1+52−1−52−1−52000000000000
χ3944-44444440-4-4-44444-2-2000000000-4-42-2-2-2-200000000000000000000220000000000000000
χ4044-4−1−5−1+5−1−5−1+54401+51−5-4−1−5−1+5−1−5−1+5440000000001+51−5-4−1−5−1+5−1−5−1+5000000000000000000001+51−50000000000000000
χ4144-4−1−5−1+5−1−5−1+54401+51−5-4−1−5−1+5−1−5−1+5-2-20000000001+51−521+521−521+521−5200000000000000000000−1−52−1+52ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116000000000000
χ4244-4−1−5−1+5−1−5−1+54401+51−5-4−1−5−1+5−1−5−1+5-2-20000000001+51−521+521−521+521−5200000000000000000000−1−52−1+52−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116000000000000
χ4344-4−1+5−1−5−1+5−1−54401−51+5-4−1+5−1−5−1+5−1−5440000000001−51+5-4−1+5−1−5−1+5−1−5000000000000000000001−51+50000000000000000
χ4444-4−1+5−1−5−1+5−1−54401−51+5-4−1+5−1−5−1+5−1−5-2-20000000001−51+521−521+521−521+5200000000000000000000−1+52−1−52−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92000000000000
χ4544-4−1+5−1−5−1+5−1−54401−51+5-4−1+5−1−5−1+5−1−5-2-20000000001−51+521−521+521−521+5200000000000000000000−1+52−1−52ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92000000000000
χ464-4044-4-4-44000044-4-4-2200−2i22i200000000-2-22200000000000000000−2i22i200000000000000i2−i2000
χ474-4044-4-4-44000044-4-4-22002i2−2i200000000-2-222000000000000000002i2−2i200000000000000−i2i2000
χ484-40−1−5−1+51+51−5-440000−1−5−1+51+51−54-40000022−2222−22000−1−5−1+51+51−500000−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+ζ119−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+ζ1190000000000000000000000000
χ494-40−1−5−1+51+51−5-440000−1−5−1+51+51−54-400000−2222−2222000−1−5−1+51+51−500000ζ7−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−ζ119ζ7−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−ζ1190000000000000000000000000
χ504-40−1+5−1−51−51+5-440000−1+5−1−51−51+54-40000022−2222−22000−1+5−1−51−51+500000ζ29−ζ31+ζ61−ζ71−ζ79+ζ101+ζ109−ζ119−ζ29+ζ31−ζ61+ζ71+ζ79−ζ101−ζ109+ζ119−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+ζ119−ζ7+ζ13−ζ23+ζ37−ζ47+ζ53+ζ77−ζ103ζ7−ζ13+ζ23−ζ37+ζ47−ζ53−ζ77+ζ1030000000000000000000000000
χ514-40−1+5−1−51−51+5-440000−1+5−1−51−51+54-400000−2222−2222000−1+5−1−51−51+500000−ζ29+ζ31−ζ61+ζ71+ζ79−ζ101−ζ109+ζ119ζ29−ζ31+ζ61−ζ71−ζ79+ζ101+ζ109−ζ119ζ7−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−ζ119ζ7−ζ13+ζ23−ζ37+ζ47−ζ53−ζ77+ζ103−ζ7+ζ13−ζ23+ζ37−ζ47+ζ53+ζ77−ζ1030000000000000000000000000
χ52666−3−352−3+352−3−352−3+352-2-26−3−352−3+352-21+521−521+521−5200−3−352−3+35200-222-2-21+521−520000002-21+521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000−1−52−1+521+521−5200000000
χ53666−3−352−3+352−3−352−3+352-2-26−3−352−3+352-21+521−521+521−5200−3−352−3+35200-2-2-2221+521−52000000-221+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000000001+521−52−1−52−1+5200000000
χ54666−3−352−3+352−3−352−3+352-2-2-6−3−352−3+352-21+521−521+521−52003+3523−35200222-2-21+521−52000000-22−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000000001+521−52−1−52−1+5200000000
χ55666−3−352−3+352−3−352−3+352-2-2-6−3−352−3+352-21+521−521+521−52003+3523−352002-2-2221+521−520000002-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000−1−52−1+521+521−5200000000
χ56666−3+352−3−352−3+352−3−352-2-26−3+352−3−352-21−521+521−521+5200−3+352−3−35200-222-2-21−521+520000002-21−521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000−1+52−1−521−521+5200000000
χ57666−3+352−3−352−3+352−3−352-2-26−3+352−3−352-21−521+521−521+5200−3+352−3−35200-2-2-2221−521+52000000-221−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000001−521+52−1+52−1−5200000000
χ58666−3+352−3−352−3+352−3−352-2-2-6−3+352−3−352-21−521+521−521+52003−3523+35200222-2-21−521+52000000-22−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000000001−521+52−1+52−1−5200000000
χ59666−3+352−3−352−3+352−3−352-2-2-6−3+352−3−352-21−521+521−521+52003−3523+352002-2-2221−521+520000002-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000−1+52−1−521−521+5200000000
χ6066-66666-2-20-6-62-2-2-2-2000000000002200000000000000000022-2-200000000000000-2200000
χ6166-66666-2-20-6-62-2-2-2-20000000000022000000000000000000-2-222000000000000002-200000
χ626-6066-6-62-20000-2-2220000−3i23i202−2−220000000000002−22−2−22−222i−2i−2i2ii2−i20000000000000000000
χ636-6066-6-62-20000-2-2220000−3i23i20−222−2000000000000−22−222−22−2−2i2i2i−2ii2−i20000000000000000000
χ646-6066-6-62-20000-2-22200003i2−3i202−2−220000000000002−22−2−22−22−2i2i2i−2i−i2i20000000000000000000
χ656-6066-6-62-20000-2-22200003i2−3i20−222−2000000000000−22−222−22−22i−2i−2i2i−i2i20000000000000000000
χ668-80−2−25−2+252+252−25-880000−2−25−2+252+252−25-440000000000001+51−5−1−5−1+500000000000000000000000000000000000000
χ678-80−2+25−2−252−252+25-880000−2+25−2−252−252+25-440000000000001−51+5−1+5−1−500000000000000000000000000000000000000
χ681212-12−3−35−3+35−3−35−3+35-4-403+353−3541+51−51+51−500000000000−1−5−1+50000000000000000000000000000000000000000000
χ691212-12−3+35−3−35−3+35−3−35-4-403−353+3541−51+51−51+500000000000−1+5−1−50000000000000000000000000000000000000000000
χ7012-120−3−35−3+353+353−354-400001+51−5−1−5−1+5000000022−22−2222000000000000−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+ζ119ζ7−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−ζ1190000000000000000000000000
χ7112-120−3−35−3+353+353−354-400001+51−5−1−5−1+50000000−222222−22000000000000ζ7−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−ζ119−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+ζ1190000000000000000000000000
χ7212-120−3+35−3−353−353+354-400001−51+5−1+5−1−5000000022−22−2222000000000000ζ29−ζ31+ζ61−ζ71−ζ79+ζ101+ζ109−ζ119−ζ29+ζ31−ζ61+ζ71+ζ79−ζ101−ζ109+ζ119−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−ζ119ζ7−ζ13+ζ23−ζ37+ζ47−ζ53−ζ77+ζ103−ζ7+ζ13−ζ23+ζ37−ζ47+ζ53+ζ77−ζ1030000000000000000000000000
χ7312-120−3+35−3−353−353+354-400001−51+5−1+5−1−50000000−222222−22000000000000−ζ29+ζ31−ζ61+ζ71+ζ79−ζ101−ζ109+ζ119ζ29−ζ31+ζ61−ζ71−ζ79+ζ101+ζ109−ζ119ζ7−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+ζ119−ζ7+ζ13−ζ23+ζ37−ζ47+ζ53+ζ77−ζ103ζ7−ζ13+ζ23−ζ37+ζ47−ζ53−ζ77+ζ1030000000000000000000000000

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