Finite Group Databasebeta

← Group #14511608

Character table — Group #14511608

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1122223366666610121212121224242424242424242424242424243030303232484848486064646464120120120120160160
order125510102244101010104420202020448820204040404040404040444362020202041515303044881212
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111
χ311111111111111-11111111111111111111-1-1-1111111-11111-1-1-1-1-1-1
χ411111111111111-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1
χ52222222222222222222200002200000000222-1-100002-1-1-1-10000-1-1
χ622222222222222-22222200002200000000-2-2-2-1-10000-2-1-1-1-1000011
χ722−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+5202−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200022−1−52−1+52−1−52−1+520−1−52−1+52−1−52−1+52000000
χ822−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+5202−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+521+521+521+521+521−521−521−521−52000221+521−521+521−520−1−52−1+52−1−52−1+52000000
χ922−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−5202−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200022−1+52−1−52−1+52−1−520−1+52−1−52−1+52−1−52000000
χ1022−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−5202−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−521−521−521−521−521+521+521+521+52000221−521+521−521+520−1+52−1−52−1+52−1−52000000
χ1133333333-1-133333-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-13-1-1001111-1000011-1-100
χ1233333333-1-133333-1-1-1-1-1-1-111-1-1111111113-1-100-1-1-1-1-10000-1-11100
χ1333333333-1-13333-3-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-31100111110000-1-11100
χ1433333333-1-13333-3-1-1-1-1-1-1-111-1-111111111-31100-1-1-1-11000011-1-100
χ15333333-1-1−1+2i−1−2i-1-1-1-131−1+2i−1−2i−1+2i−1−2i1-1i−i11ii−i−iii−i−i-1−1+2i−1−2i0011-1-1100001-1i−i00
χ16333333-1-1−1+2i−1−2i-1-1-1-131−1+2i−1−2i−1+2i−1−2i-11−ii11−i−iii−i−iii-1−1+2i−1−2i00-1-11110000-11−ii00
χ17333333-1-1−1+2i−1−2i-1-1-1-1-31−1+2i−1−2i−1+2i−1−2i1-1i−i11ii−i−iii−i−i11−2i1+2i0011-1-1-10000-11−ii00
χ18333333-1-1−1+2i−1−2i-1-1-1-1-31−1+2i−1−2i−1+2i−1−2i-11−ii11−i−iii−i−iii11−2i1+2i00-1-111-100001-1i−i00
χ19333333-1-1−1−2i−1+2i-1-1-1-131−1−2i−1+2i−1−2i−1+2i1-1−ii11−i−iii−i−iii-1−1−2i−1+2i0011-1-1100001-1−ii00
χ20333333-1-1−1−2i−1+2i-1-1-1-131−1−2i−1+2i−1−2i−1+2i-11i−i11ii−i−iii−i−i-1−1−2i−1+2i00-1-11110000-11i−i00
χ21333333-1-1−1−2i−1+2i-1-1-1-1-31−1−2i−1+2i−1−2i−1+2i1-1−ii11−i−iii−i−iii11+2i1−2i0011-1-1-10000-11i−i00
χ22333333-1-1−1−2i−1+2i-1-1-1-1-31−1−2i−1+2i−1−2i−1+2i-11i−i11ii−i−iii−i−i11+2i1−2i00-1-111-100001-1−ii00
χ2344−1−5−1+5−1−5−1+54444−1−5−1+5−1−5−1+504−1−5−1−5−1+5−1+50000−1−5−1+500000000000-2-2000001+521−521+521−52000000
χ2444−1+5−1−5−1+5−1−54444−1+5−1−5−1+5−1−504−1+5−1+5−1−5−1−50000−1+5−1−500000000000-2-2000001−521+521−521+52000000
χ254-444-4-44-40044-4-4000000000000000000000001-10000011-1-100003−3
χ264-444-4-44-40044-4-4000000000000000000000001-10000011-1-10000−33
χ274-444-4-44-40044-4-400000000000000000000000-2200000-2-222000000
χ284-4−1−5−1+51+51−54-400−1−5−1+51+51−5000000000000−ζ7−ζ13+ζ23+ζ37−ζ47−ζ53+ζ77+ζ103ζ7+ζ13−ζ23−ζ37+ζ47+ζ53−ζ77−ζ103−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+ζ119ζ29+ζ31−ζ61+ζ71−ζ79−ζ101+ζ109−ζ119−ζ29−ζ31+ζ61−ζ71+ζ79+ζ101−ζ109+ζ119000-22000001+521−52−1−52−1+52000000
χ294-4−1−5−1+51+51−54-400−1−5−1+51+51−5000000000000ζ7+ζ13−ζ23−ζ37+ζ47+ζ53−ζ77−ζ103−ζ7−ζ13+ζ23+ζ37−ζ47−ζ53+ζ77+ζ103ζ7+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−ζ29−ζ31+ζ61−ζ71+ζ79+ζ101−ζ109+ζ119ζ29+ζ31−ζ61+ζ71−ζ79−ζ101+ζ109−ζ119000-22000001+521−52−1−52−1+52000000
χ304-4−1+5−1−51−51+54-400−1+5−1−51−51+5000000000000ζ29+ζ31−ζ61+ζ71−ζ79−ζ101+ζ109−ζ119−ζ29−ζ31+ζ61−ζ71+ζ79+ζ101−ζ109+ζ119ζ29+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+ζ103ζ7+ζ13−ζ23−ζ37+ζ47+ζ53−ζ77−ζ103−ζ7−ζ13+ζ23+ζ37−ζ47−ζ53+ζ77+ζ103000-22000001−521+52−1+52−1−52000000
χ314-4−1+5−1−51−51+54-400−1+5−1−51−51+5000000000000−ζ29−ζ31+ζ61−ζ71+ζ79+ζ101−ζ109+ζ119ζ29+ζ31−ζ61+ζ71−ζ79−ζ101+ζ109−ζ119−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−ζ7−ζ13+ζ23+ζ37−ζ47−ζ53+ζ77+ζ103ζ7+ζ13−ζ23−ζ37+ζ47+ζ53−ζ77−ζ103000-22000001−521+52−1+52−1−52000000
χ32666666-2-222-2-2-2-26-222220000-2-200000000-222000000-20000000000
χ33666666-2-222-2-2-2-2-6-222220000-2-2000000002-2-200000020000000000
χ3466−3−352−3+352−3−352−3+35266-2-2−3−352−3+352−3−352−3+3520-21+521+521−521−5222-2-21+521−521+521+521+521+521−521−521−521−5200000−1−52−1+52−1−52−1+5200000000000
χ3566−3−352−3+352−3−352−3+35266-2-2−3−352−3+352−3−352−3+3520-21+521+521−521−52-2-2221+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000001+521−521+521−5200000000000
χ3666−3−352−3+352−3−352−3+352-2-2−2+4i−2−4i1+521−521+521−5202−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ1182ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ116−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ1162-22i−2i−1−52−1+52−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ9400000−1−52−1+521+521−5200000000000
χ3766−3−352−3+352−3−352−3+352-2-2−2+4i−2−4i1+521−521+521−5202−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ1182ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ116−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116-22−2i2i−1−52−1+52ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94000001+521−52−1−52−1+5200000000000
χ3866−3−352−3+352−3−352−3+352-2-2−2−4i−2+4i1+521−521+521−52022ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ118−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ1162-2−2i2i−1−52−1+52ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ9400000−1−52−1+521+521−5200000000000
χ3966−3−352−3+352−3−352−3+352-2-2−2−4i−2+4i1+521−521+521−52022ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ118−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ116-222i−2i−1−52−1+52−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94000001+521−52−1−52−1+5200000000000
χ4066−3+352−3−352−3+352−3−35266-2-2−3+352−3−352−3+352−3−3520-21−521−521+521+5222-2-21−521+521−521−521−521−521+521+521+521+5200000−1+52−1−52−1+52−1−5200000000000
χ4166−3+352−3−352−3+352−3−35266-2-2−3+352−3−352−3+352−3−3520-21−521−521+521+52-2-2221−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000001−521+521−521+5200000000000
χ4266−3+352−3−352−3+352−3−352-2-2−2+4i−2−4i1−521+521−521+5202−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ116−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ1182ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ1182-22i−2i−1+52−1−52−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ11800000−1+52−1−521−521+5200000000000
χ4366−3+352−3−352−3+352−3−352-2-2−2+4i−2−4i1−521+521−521+5202−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ116−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ1182ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118-22−2i2i−1+52−1−52ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118000001−521+52−1+52−1−5200000000000
χ4466−3+352−3−352−3+352−3−352-2-2−2−4i−2+4i1−521+521−521+5202−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ1162ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ1182-2−2i2i−1+52−1−52ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ11800000−1+52−1−521−521+5200000000000
χ4566−3+352−3−352−3+352−3−352-2-2−2−4i−2+4i1−521+521−521+5202−ζ4+2ζ14−ζ44+2ζ46−ζ76+2ζ86+2ζ94−ζ116−ζ4−2ζ14−ζ44−2ζ46−ζ76−2ζ86−2ζ94−ζ1162ζ22−ζ28+2ζ38−ζ52+2ζ62−ζ68−ζ92+2ζ118−2ζ22−ζ28−2ζ38−ζ52−2ζ62−ζ68−ζ92−2ζ118-222i−2i−1+52−1−52−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118000001−521+52−1+52−1−5200000000000
χ468-8−2−25−2+252+252−258-800−2−25−2+252+252−25000000000000000000000002-200000−1−52−1+521+521−52000000
χ478-8−2+25−2−252−252+258-800−2+25−2−252−252+25000000000000000000000002-200000−1+52−1−521−521+52000000
χ481212−3−35−3+35−3−35−3+35-4-4441+51−51+51−50-4−1−5−1−5−1+5−1+500001+51−50000000000000000000000000000
χ491212−3+35−3−35−3+35−3−35-4-4441−51+51−51+50-4−1+5−1+5−1−5−1−500001−51+50000000000000000000000000000
χ5012-121212-12-12-4400-4-4440000000000000000000000000000000000000000
χ5112-12−3−35−3+353+353−35-44001+51−5−1−5−1+5000000000000ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103−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−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ119ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ11900000000000000000000
χ5212-12−3−35−3+353+353−35-44001+51−5−1−5−1+5000000000000−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103ζ7−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+ζ119ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ119−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ11900000000000000000000
χ5312-12−3+35−3−353−353+35-44001−51+5−1+5−1−5000000000000−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ119ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ119ζ29−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−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ103ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ10300000000000000000000
χ5412-12−3+35−3−353−353+35-44001−51+5−1+5−1−5000000000000ζ29−ζ31−ζ61−ζ71+ζ79−ζ101+ζ109+ζ119−ζ29+ζ31+ζ61+ζ71−ζ79+ζ101−ζ109−ζ119−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−ζ103ζ7−ζ13−ζ23+ζ37+ζ47−ζ53+ζ77−ζ103−ζ7+ζ13+ζ23−ζ37−ζ47+ζ53−ζ77+ζ10300000000000000000000

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