Finite Group Databasebeta

← Group #11752052

Character table — Group #11752052

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444445555666688888888101010101010121212121212121220202020202020202020202020203030303060606060
order1222223666566101010101010104444444415303030303030304412121212202020202020202088881212242424242424242422228888
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
χ91111-1-111111-1-111-1-1-1-11111111-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-11-11-1
χ101111-1-111111-1-111-1-1-1-11111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-11-11
χ111111-1-111111-1-111-1-1-1-111111-1-1111111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-1-1-1-111-11-11
χ121111-1-111111-1-111-1-1-1-111111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1-1-111-1-111-1-1111-11-1
χ131111-1-111111-1-111-1-1-1-11-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1i−i−ii11ii−i−i−i−iii-1-111i−i−ii
χ141111-1-111111-1-111-1-1-1-11-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1−iii−i11−i−iiiii−i−i-1-111−iii−i
χ151111-1-111111-1-111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111i−i−ii11ii−i−i−i−iii11-1-1−iii−i
χ161111-1-111111-1-111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111−iii−i11−i−iiiii−i−i11-1-1i−i−ii
χ17222222-1-1-1-12-1-1222222222220000-1-1-1-1-1-1-1-122-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-100000000
χ18222222-1-1-1-12-1-1222222222220000-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2-2-2-1-11111111100000000
χ19222222-1-1-1-12-1-12222222-2-2-2-20000-1-1-1-1-1-1-1-1-2-21111000000002i2i−2i−2i11−i−i−i−iiiii00000000
χ20222222-1-1-1-12-1-12222222-2-2-2-20000-1-1-1-1-1-1-1-1-2-2111100000000−2i−2i2i2i11iiii−i−i−i−i00000000
χ212222-2-2-1-1-1-121122-2-2-2-2222220000-1-1-1-11111-2-2-1-1-1-1000000002-22-211-1-111-1-11100000000
χ222222-2-2-1-1-1-121122-2-2-2-2222220000-1-1-1-11111-2-2-1-1-1-100000000-22-221111-1-111-1-100000000
χ232222-2-2-1-1-1-121122-2-2-2-22-2-2-2-20000-1-1-1-11111221111000000002i−2i−2i2i-1-1−i−iiiii−i−i00000000
χ242222-2-2-1-1-1-121122-2-2-2-22-2-2-2-20000-1-1-1-1111122111100000000−2i2i2i−2i-1-1ii−i−i−i−iii00000000
χ2522-2-20022-2-22002-20000-22i2i−2i−2i002i−2i22-2-20000002i2i−2i−2i00002i2i−2i−2i00000000000000002-20000
χ2622-2-20022-2-22002-20000-22i2i−2i−2i00−2i2i22-2-20000002i2i−2i−2i0000−2i−2i2i2i0000000000000000-220000
χ2722-2-20022-2-22002-20000-2−2i−2i2i2i002i−2i22-2-2000000−2i−2i2i2i00002i2i−2i−2i0000000000000000-220000
χ2822-2-20022-2-22002-20000-2−2i−2i2i2i00−2i2i22-2-2000000−2i−2i2i2i0000−2i−2i2i2i00000000000000002-20000
χ292-22-22-22-22-222-2-2222-2-2-22i−2i2i−2i00002-22-222-2-22i−2i2i−2i2i−2i0000000000002i−2i0000000000000000
χ302-22-22-22-22-222-2-2222-2-2-2−2i2i−2i2i00002-22-222-2-2−2i2i−2i2i−2i2i000000000000−2i2i0000000000000000
χ312-22-22-2-11-112-11-2222-2-2-22i−2i2i−2i0000-11-11-1-1112i−2i−ii−ii000000000000−iiζ7−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
χ322-22-22-2-11-112-11-2222-2-2-22i−2i2i−2i0000-11-11-1-1112i−2i−ii−ii000000000000−ii−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
χ332-22-22-2-11-112-11-2222-2-2-2−2i2i−2i2i0000-11-11-1-111−2i2ii−ii−i000000000000i−iζ13−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
χ342-22-22-2-11-112-11-2222-2-2-2−2i2i−2i2i0000-11-11-1-111−2i2ii−ii−i000000000000i−i−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
χ352-22-2-222-22-22-22-22-2-222-22i−2i2i−2i00002-22-2-2-222−2i2i2i−2i2i−2i000000000000−2i2i0000000000000000
χ362-22-2-222-22-22-22-22-2-222-2−2i2i−2i2i00002-22-2-2-2222i−2i−2i2i−2i2i0000000000002i−2i0000000000000000
χ372-22-2-22-11-1121-1-22-2-222-22i−2i2i−2i0000-11-1111-1-1−2i2i−ii−ii000000000000i−iζ7−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
χ382-22-2-22-11-1121-1-22-2-222-22i−2i2i−2i0000-11-1111-1-1−2i2i−ii−ii000000000000i−i−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
χ392-22-2-22-11-1121-1-22-2-222-2−2i2i−2i2i0000-11-1111-1-12i−2ii−ii−i000000000000−iiζ13−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
χ402-22-2-22-11-1121-1-22-2-222-2−2i2i−2i2i0000-11-1111-1-12i−2ii−ii−i000000000000−ii−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
χ412-2-22002-2-22200-2-2000022-2-222-2002-2-220000002-2-2222-2-20000000000000000002-2000000
χ422-2-22002-2-22200-2-2000022-2-22-22002-2-220000002-2-22-2-222000000000000000000-22000000
χ432-2-22002-2-22200-2-200002-222-22-2002-2-22000000-222-222-2-2000000000000000000-22000000
χ442-2-22002-2-22200-2-200002-222-2-22002-2-22000000-222-2-2-2220000000000000000002-2000000
χ454444444444-144-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-144-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1000000111111110000000000000000000000
χ474444-4-44444-1-4-4-1-11111-1000044-4-4-1-1-1-11111000000-1-1-1-111110000000000000000000000
χ484444-4-44444-1-4-4-1-11111-10000-4-444-1-1-1-111110000001111-1-1-1-10000000000000000000000
χ4944-4-40044-4-4-100-11−55−5510000004i−4i-1-111−55−55000000−i5i5−i5i5−i−iii0000000000000000000000
χ5044-4-40044-4-4-100-11−55−551000000−4i4i-1-111−55−55000000i5−i5i5−i5ii−i−i0000000000000000000000
χ5144-4-40044-4-4-100-115−55−510000004i−4i-1-1115−55−5000000i5−i5i5−i5−i−iii0000000000000000000000
χ5244-4-40044-4-4-100-115−55−51000000−4i4i-1-1115−55−5000000−i5i5−i5i5ii−i−i0000000000000000000000
χ5344-4-400-2-2224004-40000-44i4i−4i−4i0000-2-222000000−2i−2i2i2i000000000000000000000000000000
χ5444-4-400-2-2224004-40000-4−4i−4i4i4i0000-2-2220000002i2i−2i−2i000000000000000000000000000000
χ554-44-44-44-44-4-14-41-1-1-111100000000-11-11-1-111000000−i5i5i5−i5−i5i5−i5i50000000000000000000000
χ564-44-44-44-44-4-14-41-1-1-111100000000-11-11-1-111000000i5−i5−i5i5i5−i5i5−i50000000000000000000000
χ574-44-4-444-44-4-1-441-111-1-1100000000-11-1111-1-1000000−i5i5i5−i5i5−i5i5−i50000000000000000000000
χ584-44-4-444-44-4-1-441-111-1-1100000000-11-1111-1-1000000i5−i5−i5i5−i5i5−i5i50000000000000000000000
χ594-4-44004-4-44-10011−555−5-100004-400-111-1−555−5000000-1-111−555−50000000000000000000000
χ604-4-44004-4-44-10011−555−5-10000-4400-111-1−555−500000011-1-15−5−550000000000000000000000
χ614-4-44004-4-44-100115−5−55-100004-400-111-15−5−55000000-1-1115−5−550000000000000000000000
χ624-4-44004-4-44-100115−5−55-10000-4400-111-15−5−5500000011-1-1−555−50000000000000000000000
χ634-4-4400-222-2400-4-4000044-4-440000-222-2000000-222-2000000000000000000000000000000
χ644-4-4400-222-2400-4-400004-444-40000-222-20000002-2-22000000000000000000000000000000
χ65888888-4-4-4-4-2-4-4-2-2-2-2-2-2-20000000011111111000000000000000000000000000000000000
χ668888-8-8-4-4-4-4-244-2-22222-2000000001111-1-1-1-1000000000000000000000000000000000000
χ6788-8-800-4-444-200-22−2525−252520000000011-1-15−55−5000000000000000000000000000000000000
χ6888-8-800-4-444-200-2225−2525−2520000000011-1-1−55−55000000000000000000000000000000000000
χ698-88-88-8-44-44-2-442-2-2-2222000000001-11-111-1-1000000000000000000000000000000000000
χ708-88-8-88-44-44-24-42-222-2-22000000001-11-1-1-111000000000000000000000000000000000000
χ718-8-8800-444-4-20022−252525−25-2000000001-1-115−5−55000000000000000000000000000000000000
χ728-8-8800-444-4-2002225−25−2525-2000000001-1-11−555−5000000000000000000000000000000000000

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