Finite Group Databasebeta

← Group #1193

Character table — Group #1193

Order 120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size1111222222222222222222222222222215151515
order124435561010121215151515202020203030303060606060606060608888
χ1111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1
χ311-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−i
χ411-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii
χ51-1i−i111-1-1-1i−i1111ii−i−i-1-1-1-1iiii−i−i−i−iζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109
χ61-1i−i111-1-1-1i−i1111ii−i−i-1-1-1-1iiii−i−i−i−i−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109
χ71-1−ii111-1-1-1−ii1111−i−iii-1-1-1-1−i−i−i−iiiii−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119
χ81-1−ii111-1-1-1−ii1111−i−iii-1-1-1-1−i−i−i−iiiiiζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119
χ922222−1−52−1+522−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000
χ1022222−1+52−1−522−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000
χ112222-122-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000
χ122222-1−1−52−1+52-1−1−52−1+52-1-1−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−1−52−1+52−1−52−1+52−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1160000
χ132222-1−1−52−1+52-1−1−52−1+52-1-1−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−1−52−1+52−1−52−1+52−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ760000
χ142222-1−1+52−1−52-1−1+52−1−52-1-1−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−1+52−1−52−1+52−1−52−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ680000
χ152222-1−1+52−1−52-1−1+52−1−52-1-1−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−1+52−1−52−1+52−1−52−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ920000
χ1622-2-22−1−52−1+522−1−52−1+52-2-2−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000
χ1722-2-22−1+52−1−522−1+52−1−52-2-2−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000
χ1822-2-2-122-12211-1-1-1-1-2-2-2-2-1-1-1-1111111110000
χ1922-2-2-1−1−52−1+52-1−1−52−1+5211−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1161+521−521+521−52−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ1160000
χ2022-2-2-1−1−52−1+52-1−1−52−1+5211−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ761+521−521+521−52−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ760000
χ2122-2-2-1−1+52−1−52-1−1+52−1−5211−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ681−521+521−521+52−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ680000
χ2222-2-2-1−1+52−1−52-1−1+52−1−5211−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ921−521+521−521+52−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ920000
χ232-22i−2i2−1−52−1+52-21+521−522i−2i−1−52−1−52−1+52−1+52−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ941+521+521−521−52−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ940000
χ242-22i−2i2−1+52−1−52-21−521+522i−2i−1+52−1+52−1−52−1−52−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ1181−521−521+521+52−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ1180000
χ252-22i−2i-1221-2-2−ii-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000
χ262-22i−2i-1−1−52−1+5211+521−52−ii−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116ζ22+ζ38ζ62+ζ118ζ14+ζ46ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ940000
χ272-22i−2i-1−1−52−1+5211+521−52−ii−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76ζ62+ζ118ζ22+ζ38ζ86+ζ94ζ14+ζ46−ζ62−ζ118−ζ22−ζ38−ζ86−ζ94−ζ14−ζ460000
χ282-22i−2i-1−1+52−1−5211−521+52−ii−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68ζ14+ζ46ζ86+ζ94ζ62+ζ118ζ22+ζ38−ζ14−ζ46−ζ86−ζ94−ζ62−ζ118−ζ22−ζ380000
χ292-22i−2i-1−1+52−1−5211−521+52−ii−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92ζ86+ζ94ζ14+ζ46ζ22+ζ38ζ62+ζ118−ζ86−ζ94−ζ14−ζ46−ζ22−ζ38−ζ62−ζ1180000
χ302-2−2i2i2−1−52−1+52-21+521−52−2i2i−1−52−1−52−1+52−1+52ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ941+521+521−521−52ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ940000
χ312-2−2i2i2−1+52−1−52-21−521+52−2i2i−1+52−1+52−1−52−1−52ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ1181−521−521+521+52ζ14+ζ46+ζ86+ζ94ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118−ζ22−ζ38−ζ62−ζ1180000
χ322-2−2i2i-1221-2-2i−i-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000
χ332-2−2i2i-1−1−52−1+5211+521−52i−i−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ22+ζ38ζ62+ζ118ζ14+ζ46ζ86+ζ940000
χ342-2−2i2i-1−1−52−1+5211+521−52i−i−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76ζ22+ζ38+ζ62+ζ118ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76−ζ62−ζ118−ζ22−ζ38−ζ86−ζ94−ζ14−ζ46ζ62+ζ118ζ22+ζ38ζ86+ζ94ζ14+ζ460000
χ352-2−2i2i-1−1+52−1−5211−521+52i−i−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68−ζ14−ζ46−ζ86−ζ94−ζ62−ζ118−ζ22−ζ38ζ14+ζ46ζ86+ζ94ζ62+ζ118ζ22+ζ380000
χ362-2−2i2i-1−1+52−1−5211−521+52i−i−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92ζ14+ζ46+ζ86+ζ94ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94−ζ22−ζ38−ζ62−ζ118ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92−ζ86−ζ94−ζ14−ζ46−ζ22−ζ38−ζ62−ζ118ζ86+ζ94ζ14+ζ46ζ22+ζ38ζ62+ζ1180000

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