Finite Group Databasebeta

← Group #11751922

Character table — Group #11751922

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444445555666688888888101010101010121212121212121220202020202020202020202020203030303060606060
order122234466651010101212202020204444444415303030606060604412121212202020202020202088881212242424242424242422448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ611111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i1111−i−iii
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii1111ii−i−i
χ911111-1-11111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-11-11-1
χ1011111-1-11111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-11-11
χ1111111-1-11111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-1-1-1-111-11-11
χ1211111-1-11111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1-1-111-1-111-1-1111-11-1
χ1311111-1-11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1i−i−ii11ii−i−i−i−iii-1-111i−i−ii
χ1411111-1-11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1−iii−i11−i−iiiii−i−i-1-111−iii−i
χ1511111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111i−i−ii11ii−i−i−i−iii11-1-1−iii−i
χ1611111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111−iii−i11−i−iiiii−i−i11-1-1i−i−ii
χ172222-122-1-1-12222-1-1222222220000-1-1-1-1-1-1-1-122-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-100000000
χ182222-122-1-1-12222-1-1222222220000-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2-2-2-1-11111111100000000
χ192222-122-1-1-12222-1-12222-2-2-2-20000-1-1-1-1-1-1-1-1-2-21111000000002i2i−2i−2i11−i−i−i−iiiii00000000
χ202222-122-1-1-12222-1-12222-2-2-2-20000-1-1-1-1-1-1-1-1-2-2111100000000−2i−2i2i2i11iiii−i−i−i−i00000000
χ212222-1-2-2-1-1-1222211-2-2-2-222220000-1-1-1-11111-2-2-1-1-1-1000000002-22-211-1-111-1-11100000000
χ222222-1-2-2-1-1-1222211-2-2-2-222220000-1-1-1-11111-2-2-1-1-1-100000000-22-221111-1-111-1-100000000
χ232222-1-2-2-1-1-1222211-2-2-2-2-2-2-2-20000-1-1-1-11111221111000000002i−2i−2i2i-1-1−i−iiiii−i−i00000000
χ242222-1-2-2-1-1-1222211-2-2-2-2-2-2-2-20000-1-1-1-1111122111100000000−2i2i2i−2i-1-1ii−i−i−i−iii00000000
χ2522-2-2200-22-22-22-200000022-2-22-20022-2-200000022-2-222-2-20000000000000000002-2000000
χ2622-2-2200-22-22-22-200000022-2-2-220022-2-200000022-2-2-2-222000000000000000000-22000000
χ2722-2-2200-22-22-22-2000000-2-2222-20022-2-2000000-2-22222-2-2000000000000000000-22000000
χ2822-2-2200-22-22-22-2000000-2-222-220022-2-2000000-2-222-2-2220000000000000000002-2000000
χ292-22-2200-2-222-2-220000002i−2i2i−2i002-22-22-20000002i−2i2i−2i000022-2-200000000000000002i−2i0000
χ302-22-2200-2-222-2-220000002i−2i2i−2i00-222-22-20000002i−2i2i−2i0000-2-2220000000000000000−2i2i0000
χ312-22-2200-2-222-2-22000000−2i2i−2i2i002-22-22-2000000−2i2i−2i2i000022-2-20000000000000000−2i2i0000
χ322-22-2200-2-222-2-22000000−2i2i−2i2i00-222-22-2000000−2i2i−2i2i0000-2-22200000000000000002i−2i0000
χ332-2-2222-22-2-222-2-22-222-2-22i−2i−2i2i00002-2-2222-2-22i−2i2i−2i−2i2i0000000000002i−2i0000000000000000
χ342-2-2222-22-2-222-2-22-222-2-2−2i2i2i−2i00002-2-2222-2-2−2i2i−2i2i2i−2i000000000000−2i2i0000000000000000
χ352-2-222-222-2-222-2-2-22-2-2222i−2i−2i2i00002-2-22-2-222−2i2i2i−2i−2i2i000000000000−2i2i0000000000000000
χ362-2-222-222-2-222-2-2-22-2-222−2i2i2i−2i00002-2-22-2-2222i−2i−2i2i2i−2i0000000000002i−2i0000000000000000
χ372-2-22-12-2-11122-2-2-1122-2-22i−2i−2i2i0000-111-1-1-1112i−2i−iii−i000000000000−iiζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ11900000000
χ382-2-22-12-2-11122-2-2-1122-2-22i−2i−2i2i0000-111-1-1-1112i−2i−iii−i000000000000−ii−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ11900000000
χ392-2-22-12-2-11122-2-2-1122-2-2−2i2i2i−2i0000-111-1-1-111−2i2ii−i−ii000000000000i−iζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ10900000000
χ402-2-22-12-2-11122-2-2-1122-2-2−2i2i2i−2i0000-111-1-1-111−2i2ii−i−ii000000000000i−i−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ10900000000
χ412-2-22-1-22-11122-2-21-1-2-2222i−2i−2i2i0000-111-111-1-1−2i2i−iii−i000000000000i−iζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−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−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ11900000000
χ422-2-22-1-22-11122-2-21-1-2-2222i−2i−2i2i0000-111-111-1-1−2i2i−iii−i000000000000i−i−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ13−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−ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ11900000000
χ432-2-22-1-22-11122-2-21-1-2-222−2i2i2i−2i0000-111-111-1-12i−2ii−i−ii000000000000−iiζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119−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−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ10900000000
χ442-2-22-1-22-11122-2-21-1-2-222−2i2i2i−2i0000-111-111-1-12i−2ii−i−ii000000000000−ii−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ7−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+ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ10900000000
χ454444444444-1-1-1-144-1-1-1-100004444-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-1-1-1-144-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1000000111111110000000000000000000000
χ4744444-4-4444-1-1-1-1-4-41111000044-4-4-1-1-1-11111000000-1-1-1-111110000000000000000000000
χ4844444-4-4444-1-1-1-1-4-411110000-4-444-1-1-1-111110000001111-1-1-1-10000000000000000000000
χ4944-4-4400-44-4-11-1100−i5i5−i5i500004-400-1-111−i5i5−i5i5000000-1-111−i5i5−i5i50000000000000000000000
χ5044-4-4400-44-4-11-1100−i5i5−i5i50000-4400-1-111−i5i5−i5i500000011-1-1i5−i5i5−i50000000000000000000000
χ5144-4-4400-44-4-11-1100i5−i5i5−i500004-400-1-111i5−i5i5−i5000000-1-111i5−i5i5−i50000000000000000000000
χ5244-4-4400-44-4-11-1100i5−i5i5−i50000-4400-1-111i5−i5i5−i500000011-1-1−i5i5−i5i50000000000000000000000
χ5344-4-4-2002-224-44-400000044-4-40000-2-222000000-2-222000000000000000000000000000000
χ5444-4-4-2002-224-44-4000000-4-4440000-2-22200000022-2-2000000000000000000000000000000
χ554-44-4400-4-44-111-100−i5i5i5−i50000004-4-11-11−i5i5i5−i5000000−i5i5−i5i5-1-1110000000000000000000000
χ564-44-4400-4-44-111-100−i5i5i5−i5000000-44-11-11−i5i5i5−i5000000i5−i5i5−i511-1-10000000000000000000000
χ574-44-4400-4-44-111-100i5−i5−i5i50000004-4-11-11i5−i5−i5i5000000i5−i5i5−i5-1-1110000000000000000000000
χ584-44-4400-4-44-111-100i5−i5−i5i5000000-44-11-11i5−i5−i5i5000000−i5i5−i5i511-1-10000000000000000000000
χ594-44-4-20022-24-4-440000004i−4i4i−4i0000-22-22000000−2i2i−2i2i000000000000000000000000000000
χ604-44-4-20022-24-4-44000000−4i4i−4i4i0000-22-220000002i−2i2i−2i000000000000000000000000000000
χ614-4-4444-44-4-4-1-1114-4-1-11100000000-111-1-1-111000000−i5i5i5−i5i5−i5−i5i50000000000000000000000
χ624-4-4444-44-4-4-1-1114-4-1-11100000000-111-1-1-111000000i5−i5−i5i5−i5i5i5−i50000000000000000000000
χ634-4-444-444-4-4-1-111-4411-1-100000000-111-111-1-1000000−i5i5i5−i5−i5i5i5−i50000000000000000000000
χ644-4-444-444-4-4-1-111-4411-1-100000000-111-111-1-1000000i5−i5−i5i5i5−i5−i5i50000000000000000000000
χ658888-488-4-4-4-2-2-2-2-4-4-2-2-2-20000000011111111000000000000000000000000000000000000
χ668888-4-8-8-4-4-4-2-2-2-2442222000000001111-1-1-1-1000000000000000000000000000000000000
χ6788-8-8-4004-44-22-2200−2i52i5−2i52i50000000011-1-1i5−i5i5−i5000000000000000000000000000000000000
χ6888-8-8-4004-44-22-22002i5−2i52i5−2i50000000011-1-1−i5i5−i5i5000000000000000000000000000000000000
χ698-88-8-40044-4-222-200−2i52i52i5−2i5000000001-11-1i5−i5−i5i5000000000000000000000000000000000000
χ708-88-8-40044-4-222-2002i5−2i5−2i52i5000000001-11-1−i5i5i5−i5000000000000000000000000000000000000
χ718-8-88-48-8-444-2-222-44-2-222000000001-1-1111-1-1000000000000000000000000000000000000
χ728-8-88-4-88-444-2-2224-422-2-2000000001-1-11-1-111000000000000000000000000000000000000

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