Finite Group Databasebeta

← Group #11751731

Character table — Group #11751731

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444445555666688888888101010101010121212121212121220202020202020202020202020203030303060606060
order1244234612125610101012202020202244888815303030606060602466121240404040404040406888812242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1ii−i−i-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ611111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1−i−iii-1−i−i−i−iiiii-1-1-1-1−i−iii
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i1111−i−iii
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii1111ii−i−i
χ911-1-1-1111-1-11-1-1-111-1-11111-1-111-1-11-1-1111-1-1-1111-1-11111-1-1-1-1-1i−ii−i1ii−i−iii−i−i11-1-1i−ii−i
χ1011-1-1-1111-1-11-1-1-111-1-11111-1-111-1-11-1-1111-1-1-1111-1-11111-1-1-1-1-1−ii−ii1−i−iii−i−iii11-1-1−ii−ii
χ1111-1-1-1111-1-11-1-1-111-1-11111-1-1-1-1111-1-1111-1-1-1111-1-1-1-1-1-11111-1i−ii−i1ii−i−iii−i−i-1-111−ii−ii
χ1211-1-1-1111-1-11-1-1-111-1-11111-1-1-1-1111-1-1111-1-1-1111-1-1-1-1-1-11111-1−ii−ii1−i−iii−i−iii-1-111i−ii−i
χ1311-1-1-1111-1-11-1-1-111-1-111-1-11111-1-11-1-1111-1-11-1-1-1111111-1-1-1-111-1-11-111-1-1-1-111-1-1111-1-11
χ1411-1-1-1111-1-11-1-1-111-1-111-1-11111-1-11-1-1111-1-11-1-1-1111111-1-1-1-11-111-1-1-1-11111-1-1-1-111-111-1
χ1511-1-1-1111-1-11-1-1-111-1-111-1-111-1-1111-1-1111-1-11-1-1-111-1-1-1-1111111-1-11-111-1-1-1-11111-1-1-111-1
χ1611-1-1-1111-1-11-1-1-111-1-111-1-111-1-1111-1-1111-1-11-1-1-111-1-1-1-111111-111-1-1-1-11111-1-111-1-11-1-11
χ1722222-12-1-1-12-1222-1222222220000-1-1-1-1-1-1-1-122-1-1-1-100000000-12222-1-1-1-1-1-1-1-1-100000000
χ1822222-12-1-1-12-1222-1222222220000-1-1-1-1-1-1-1-122-1-1-1-100000000-1-2-2-2-2-11111111100000000
χ1922222-12-1-1-12-1222-12222-2-2-2-20000-1-1-1-1-1-1-1-1-2-211110000000012i2i−2i−2i1−i−i−i−iiiii00000000
χ2022222-12-1-1-12-1222-12222-2-2-2-20000-1-1-1-1-1-1-1-1-2-21111000000001−2i−2i2i2i1iiii−i−i−i−i00000000
χ212222-22-22222-2-2-22-222-2-2222200002-2-22-2-222-2-2222200000000-20000-20000000000000000
χ222222-22-22222-2-2-22-222-2-2-2-2-2-200002-2-22-2-22222-2-2-2-2000000002000020000000000000000
χ232222-2-1-2-1-1-121-2-22122-2-222220000-111-111-1-1-2-2-1-1-1-100000000100001−i3i3−i3i3−i3i3−i3i300000000
χ242222-2-1-2-1-1-121-2-22122-2-222220000-111-111-1-1-2-2-1-1-1-100000000100001i3−i3i3−i3i3−i3i3−i300000000
χ252222-2-1-2-1-1-121-2-22122-2-2-2-2-2-20000-111-111-1-122111100000000-10000-13−33−3−33−3300000000
χ262222-2-1-2-1-1-121-2-22122-2-2-2-2-2-20000-111-111-1-122111100000000-10000-1−33−333−33−300000000
χ2722-2-222-22-2-222222-2-2-2-2-222-2-200002222-2-2-2-22-222-2-20000000020000-20000000000000000
χ2822-2-222-22-2-222222-2-2-2-2-2-2-22200002222-2-2-2-2-22-2-22200000000-2000020000000000000000
χ2922-2-22-1-2-1112-12221-2-2-2-222-2-20000-1-1-1-111112-2-1-11100000000-1000013−3−333−3−3300000000
χ3022-2-22-1-2-1112-12221-2-2-2-222-2-20000-1-1-1-111112-2-1-11100000000-100001−333−3−333−300000000
χ3122-2-22-1-2-1112-12221-2-2-2-2-2-2220000-1-1-1-11111-2211-1-10000000010000-1−i3i3i3−i3i3−i3−i3i300000000
χ3222-2-22-1-2-1112-12221-2-2-2-2-2-2220000-1-1-1-11111-2211-1-10000000010000-1i3−i3−i3i3−i3i3i3−i300000000
χ3322-2-2-2-12-11121-2-22-1-2-22222-2-20000-111-1-1-111-22-1-1110000000012i−2i2i−2i-1−i−iii−i−iii00000000
χ3422-2-2-2-12-11121-2-22-1-2-22222-2-20000-111-1-1-111-22-1-111000000001−2i2i−2i2i-1ii−i−iii−i−i00000000
χ3522-2-2-2-12-11121-2-22-1-2-222-2-2220000-111-1-1-1112-211-1-100000000-12-2-221-1-11111-1-100000000
χ3622-2-2-2-12-11121-2-22-1-2-222-2-2220000-111-1-1-1112-211-1-100000000-1-222-2111-1-1-1-11100000000
χ372-22i−2i020-22i−2i2000-202i−2i002-22i−2i2−2−i2i2200-2002i−2i002-22i−2i22−2−2−i2−i2i2i2000000000000002−2−i2i20000
χ382-22i−2i020-22i−2i2000-202i−2i002-22i−2i−22i2−i2200-2002i−2i002-22i−2i−2−222i2i2−i2−i200000000000000−22i2−i20000
χ392-22i−2i020-22i−2i2000-202i−2i00-22−2i2i2−2−i2i2200-2002i−2i00-22−2i2i22−2−2−i2−i2i2i200000000000000−22i2−i20000
χ402-22i−2i020-22i−2i2000-202i−2i00-22−2i2i−22i2−i2200-2002i−2i00-22−2i2i−2−222i2i2−i2−i2000000000000002−2−i2i20000
χ412-2−2i2i020-2−2i2i2000-20−2i2i002-2−2i2i2−2i2−i2200-200−2i2i002-2−2i2i22−2−2i2i2−i2−i2000000000000002−2i2−i20000
χ422-2−2i2i020-2−2i2i2000-20−2i2i002-2−2i2i−22−i2i2200-200−2i2i002-2−2i2i−2−222−i2−i2i2i200000000000000−22−i2i20000
χ432-2−2i2i020-2−2i2i2000-20−2i2i00-222i−2i2−2i2−i2200-200−2i2i00-222i−2i22−2−2i2i2−i2−i200000000000000−22−i2i20000
χ442-2−2i2i020-2−2i2i2000-20−2i2i00-222i−2i−22−i2i2200-200−2i2i00-222i−2i−2−222−i2−i2i2i2000000000000002−2i2−i20000
χ454444444444-14-1-1-14-1-1-1-100004444-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-14-1-1-14-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1000000111111110000000000000000000000
χ474444-44-4444-1-411-1-4-1-11100000000-111-111-1-1000000−i5i5−i5i5−i5i5−i5i50000000000000000000000
χ484444-44-4444-1-411-1-4-1-11100000000-111-111-1-1000000i5−i5i5−i5i5−i5i5−i50000000000000000000000
χ4944-4-444-44-4-4-14-1-1-1-4111100000000-1-1-1-11111000000−i5i5−i5i5i5−i5i5−i50000000000000000000000
χ5044-4-444-44-4-4-14-1-1-1-4111100000000-1-1-1-11111000000i5−i5i5−i5−i5i5−i5i50000000000000000000000
χ5144-4-4-4444-4-4-1-411-1411-1-1000044-4-4-111-1-1-111000000-1-1-1-111110000000000000000000000
χ5244-4-4-4444-4-4-1-411-1411-1-10000-4-444-111-1-1-1110000001111-1-1-1-10000000000000000000000
χ534-44i−4i040-44i−4i-10−5510−ii−i5i5000022−22−2i22i2-1−551−i5i5−ii000000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ1090000000000000000000000
χ544-44i−4i040-44i−4i-10−5510−ii−i5i50000−22222i2−2i2-1−551−i5i5−ii000000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ1090000000000000000000000
χ554-44i−4i040-44i−4i-105−510−iii5−i5000022−22−2i22i2-15−51i5−i5−ii000000ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ1190000000000000000000000
χ564-44i−4i040-44i−4i-105−510−iii5−i50000−22222i2−2i2-15−51i5−i5−ii000000−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ1190000000000000000000000
χ574-44i−4i0-202−2i2i4000-404i−4i004-44i−4i0000-200200−2i2i00-22−2i2i000000000000000000000000000000
χ584-44i−4i0-202−2i2i4000-404i−4i00-44−4i4i0000-200200−2i2i002-22i−2i000000000000000000000000000000
χ594-4−4i4i040-4−4i4i-10−5510i−ii5−i5000022−222i2−2i2-1−551i5−i5i−i000000ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ1190000000000000000000000
χ604-4−4i4i040-4−4i4i-10−5510i−ii5−i50000−2222−2i22i2-1−551i5−i5i−i000000−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ1190000000000000000000000
χ614-4−4i4i040-4−4i4i-105−510i−i−i5i5000022−222i2−2i2-15−51−i5i5i−i000000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ1090000000000000000000000
χ624-4−4i4i040-4−4i4i-105−510i−i−i5i50000−2222−2i22i2-15−51−i5i5i−i000000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ1090000000000000000000000
χ634-4−4i4i0-2022i−2i4000-40−4i4i004-4−4i4i0000-2002002i−2i00-222i−2i000000000000000000000000000000
χ644-4−4i4i0-2022i−2i4000-40−4i4i00-444i−4i0000-2002002i−2i002-2−2i2i000000000000000000000000000000
χ6588888-48-4-4-4-2-4-2-2-2-4-2-2-2-20000000011111111000000000000000000000000000000000000
χ668888-8-4-8-4-4-4-2422-24-2-222000000001-1-11-1-111000000000000000000000000000000000000
χ6788-8-88-4-8-444-2-4-2-2-242222000000001111-1-1-1-1000000000000000000000000000000000000
χ6888-8-8-8-48-444-2422-2-422-2-2000000001-1-1111-1-1000000000000000000000000000000000000
χ698-88i−8i0-404−4i4i-20−252520−2i2i−2i52i50000000015−5-1i5−i5i−i000000000000000000000000000000000000
χ708-88i−8i0-404−4i4i-2025−2520−2i2i2i5−2i5000000001−55-1−i5i5i−i000000000000000000000000000000000000
χ718-8−8i8i0-4044i−4i-20−2525202i−2i2i5−2i50000000015−5-1−i5i5−ii000000000000000000000000000000000000
χ728-8−8i8i0-4044i−4i-2025−25202i−2i−2i52i5000000001−55-1i5−i5−ii000000000000000000000000000000000000

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