Finite Group Databasebeta

← Group #14513321

Character table — Group #14513321

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size11222223344466666888812121216161616162020242424242424242424242424242432323232323232484848486060606060608080120120160
order12455101022420204101010103620204202012151530302824882020404040404040404012606060606060101020202244482424246
χ11111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1111-1-11
χ311111111111111111111111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1-111-1
χ5111111111-1111111111-1-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-11
χ6111111111-1111111111-1-1-111111111-1-1-111-1-111111111-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111
χ7111111111-1111111111-1-1-11111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1
χ8111111111-1111111111-1-1-11111111-11-1-111-1-111111111-111-1-1-1-1-1-1-1-1-11111111-1-1-1
χ922222222222222222-1-122222-1-1-1-1-12200002200000000-1-1-1-1-1-1-10000200002-1-100-1
χ1022222222222222222-1-122222-1-1-1-1-1-2-200002200000000-1-1-1-1-1-1-10000-20000-211001
χ11222222222-22222222-1-1-2-2-222-1-1-1-1-12-20000-2-2000000001-1-11111000020000-21100-1
χ12222222222-22222222-1-1-2-2-222-1-1-1-1-1-220000-2-2000000001-1-111110000-200002-1-1001
χ13222−1−52−1+52−1−52−1+52222−1−52−1+522−1−52−1+52−1−52−1+5222−1−52−1+522−1−52−1+522−1−52−1+52−1−52−1+52002222−1−52−1+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+5200000000000
χ14222−1−52−1+52−1−52−1+52222−1−52−1+522−1−52−1+52−1−52−1+5222−1−52−1+522−1−52−1+522−1−52−1+52−1−52−1+5200-2-2-2-2−1−52−1+521+521+521−521−521+521+521−521−522−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−5200000000000
χ15222−1−52−1+52−1−52−1+5222-2−1−52−1+522−1−52−1+52−1−52−1+52221+521−52-2−1−52−1+522−1−52−1+52−1−52−1+520022-2-21+521−521+521+521−521−521+521+521−521−52-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+5200000000000
χ16222−1−52−1+52−1−52−1+5222-2−1−52−1+522−1−52−1+52−1−52−1+52221+521−52-2−1−52−1+522−1−52−1+52−1−52−1+5200-2-2221+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2−1−52−1+521+521+521−521−521+521−521+521−5200000000000
χ17222−1+52−1−52−1+52−1−52222−1+52−1−522−1+52−1−52−1+52−1−5222−1+52−1−522−1+52−1−522−1+52−1−52−1+52−1−52002222−1+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+52−1−5200000000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−522−1+52−1−52−1+52−1−5222−1+52−1−522−1+52−1−522−1+52−1−52−1+52−1−5200-2-2-2-2−1+52−1−521−521−521+521+521−521−521+521+522−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+5200000000000
χ19222−1+52−1−52−1+52−1−5222-2−1+52−1−522−1+52−1−52−1+52−1−52221−521+52-2−1+52−1−522−1+52−1−52−1+52−1−520022-2-21−521+521−521−521+521+521−521−521+521+52-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−5200000000000
χ20222−1+52−1−52−1+52−1−5222-2−1+52−1−522−1+52−1−52−1+52−1−52221−521+52-2−1+52−1−522−1+52−1−52−1+52−1−5200-2-2221−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2−1+52−1−521−521−521+521+521−521+521−521+5200000000000
χ2122-22222220-2-2-2222222000-2-2-2222200000000000000000-2-20000000002-2-22000000
χ2222-22222220-2-2-2222222000-2-2-2222200000000000000000-2-2000000000-222-2000000
χ233333333-1-1333-1-1-1-1-10033-1-1-100000331-11-1-1-11111-1-1-1-1000000011-1-1-111-1-1-1001-10
χ243333333-1-1333-1-1-1-1-10033-1-1-10000033-11-11-1-1-1-1-1-111110000000-1-111-1-1-111-100-110
χ253333333-1-1333-1-1-1-1-10033-1-1-100000-3-31-11-1-1-11111-1-1-1-1000000011-1-11-1-111100-110
χ263333333-1-1333-1-1-1-1-10033-1-1-100000-3-3-11-11-1-1-1-1-1-111110000000-1-111111-1-11001-10
χ273333333-1-1-333-1-1-1-1-100-3-31-1-1000003-31-1-1111-1-1-1-11111000000011-1-1-111-1-1100-110
χ283333333-1-1-333-1-1-1-1-100-3-31-1-1000003-3-111-1111111-1-1-1-10000000-1-111-1-1-1111001-10
χ293333333-1-1-333-1-1-1-1-100-3-31-1-100000-331-1-1111-1-1-1-11111000000011-1-11-1-111-1001-10
χ303333333-1-1-333-1-1-1-1-100-3-31-1-100000-33-111-1111111-1-1-1-10000000-1-111111-1-1-100-110
χ31444−1−5−1+5−1−5−1+5444−1−5−1+54−1−5−1+5−1−5−1+5-2-2−1−5−1+54−1−5−1+5-21+521−521+521−52000000−1−5−1+500000000-21+521−521+521+521−521−52000000000000000
χ32444−1−5−1+5−1−5−1+544-4−1−5−1+54−1−5−1+5−1−5−1+5-2-21+51−5-4−1−5−1+5-21+521−521+521−520000001+51−50000000021+521−52−1−52−1−52−1+52−1+52000000000000000
χ33444−1+5−1−5−1+5−1−5444−1+5−1−54−1+5−1−5−1+5−1−5-2-2−1+5−1−54−1+5−1−5-21−521+521−521+52000000−1+5−1−500000000-21−521+521−521−521+521+52000000000000000
χ34444−1+5−1−5−1+5−1−544-4−1+5−1−54−1+5−1−5−1+5−1−5-2-21−51+5-4−1+5−1−5-21−521+521−521+520000001−51+50000000021−521+52−1+52−1+52−1−52−1−52000000000000000
χ3544-44444440-4-4-44444-2-2000-4-42-2-2-2-200000000000000000220000000000000000000
χ3644-4−1−5−1+5−1−5−1+54401+51−5-4−1−5−1+5−1−5−1+5440001+51−5-4−1−5−1+5−1−5−1+5000000000000000001+51−50000000000000000000
χ3744-4−1−5−1+5−1−5−1+54401+51−5-4−1−5−1+5−1−5−1+5-2-20001+51−521+521−521+521−5200000000000000000−1−52−1+52ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116000000000000000
χ3844-4−1−5−1+5−1−5−1+54401+51−5-4−1−5−1+5−1−5−1+5-2-20001+51−521+521−521+521−5200000000000000000−1−52−1+52−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116000000000000000
χ3944-4−1+5−1−5−1+5−1−54401−51+5-4−1+5−1−5−1+5−1−5440001−51+5-4−1+5−1−5−1+5−1−5000000000000000001−51+50000000000000000000
χ4044-4−1+5−1−5−1+5−1−54401−51+5-4−1+5−1−5−1+5−1−5-2-20001−51+521−521+521−521+5200000000000000000−1+52−1−52−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92000000000000000
χ4144-4−1+5−1−5−1+5−1−54401−51+5-4−1+5−1−5−1+5−1−5-2-20001−51+521−521+521−521+5200000000000000000−1+52−1−52ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92000000000000000
χ424-4044-4-4-440000-4-4444-400000044-4-400000000000000000000000000000000000000
χ434-4044-4-4-440000-4-444-22000000-2-2220000000000000000000000000000000006−6000
χ444-4044-4-4-440000-4-444-22000000-2-222000000000000000000000000000000000−66000
χ454-40−1−5−1+51+51−5-4400001+51−5−1−5−1+54-4000000−1−5−1+51+51−500000000ζ7−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+ζ1190000000000000000000000
χ464-40−1−5−1+51+51−5-4400001+51−5−1−5−1+54-4000000−1−5−1+51+51−500000000−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−ζ1190000000000000000000000
χ474-40−1+5−1−51−51+5-4400001−51+5−1+5−1−54-4000000−1+5−1−51−51+500000000−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−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−ζ1030000000000000000000000
χ484-40−1+5−1−51−51+5-4400001−51+5−1+5−1−54-4000000−1+5−1−51−51+500000000ζ29−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+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+ζ1030000000000000000000000
χ49666−3−352−3+352−3−352−3+352-2-26−3−352−3+352-21+521−521+521−5200−3−352−3+352-21+521−5200000002-22-21+521−52−1−52−1−52−1+52−1+521+521+521−521−520000000−1−52−1+521+521−5200000000000
χ50666−3−352−3+352−3−352−3+352-2-26−3−352−3+352-21+521−521+521−5200−3−352−3+352-21+521−520000000-22-221+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000001+521−52−1−52−1+5200000000000
χ51666−3−352−3+352−3−352−3+352-2-2-6−3−352−3+352-21+521−521+521−52003+3523−35221+521−5200000002-2-22−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000−1−52−1+521+521−5200000000000
χ52666−3−352−3+352−3−352−3+352-2-2-6−3−352−3+352-21+521−521+521−52003+3523−35221+521−520000000-222-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000001+521−52−1−52−1+5200000000000
χ53666−3+352−3−352−3+352−3−352-2-26−3+352−3−352-21−521+521−521+5200−3+352−3−352-21−521+5200000002-22-21−521+52−1+52−1+52−1−52−1−521−521−521+521+520000000−1+52−1−521−521+5200000000000
χ54666−3+352−3−352−3+352−3−352-2-26−3+352−3−352-21−521+521−521+5200−3+352−3−352-21−521+520000000-22-221−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000001−521+52−1+52−1−5200000000000
χ55666−3+352−3−352−3+352−3−352-2-2-6−3+352−3−352-21−521+521−521+52003−3523+35221−521+5200000002-2-22−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000−1+52−1−521−521+5200000000000
χ56666−3+352−3−352−3+352−3−352-2-2-6−3+352−3−352-21−521+521−521+52003−3523+35221−521+520000000-222-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000001−521+52−1+52−1−5200000000000
χ5766-66666-2-20-6-62-2-2-2-200000220000000000000000000000000000000002-22-2000000
χ5866-66666-2-20-6-62-2-2-2-20000022000000000000000000000000000000000-22-22000000
χ598-80−2−25−2+252+252−25-8800002+252−25−2−25−2+25-440000001+51−5−1−5−1+500000000000000000000000000000000000000
χ608-80−2+25−2−252−252+25-8800002−252+25−2+25−2−25-440000001−51+5−1+5−1−500000000000000000000000000000000000000
χ611212-12−3−35−3+35−3−35−3+35-4-403+353−3541+51−51+51−500000−1−5−1+50000000000000000000000000000000000000000000
χ621212-12−3+35−3−35−3+35−3−35-4-403−353+3541−51+51−51+500000−1+5−1−50000000000000000000000000000000000000000000
χ6312-1201212-12-124-4000044-4-400000000000000000000000000000000000000000000000000
χ6412-120−3−35−3+353+353−354-40000−1−5−1+51+51−500000000000000000000ζ7−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−ζ1190000000000000000000000
χ6512-120−3−35−3+353+353−354-40000−1−5−1+51+51−500000000000000000000−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+ζ1190000000000000000000000
χ6612-120−3+35−3−353−353+354-40000−1+5−1−51−51+500000000000000000000−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−ζ119ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ1030000000000000000000000
χ6712-120−3+35−3−353−353+354-40000−1+5−1−51−51+500000000000000000000ζ29−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+ζ119−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ1030000000000000000000000

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