Finite Group Databasebeta

← Group #14300393

Character table — Group #14300393

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222444444558888888881010101010101016161616161616162020202020202020202020202020202024244040404040404040484848486060606060606060120120
order1222236662456610446101010121530303044412121212102030303030606024888812122424242424242424446881224242424202020208888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1ii−i−i-1-1iiii−i−i−i−i11-1i−i-1ii−i−i1111iiii−i−i−i−i-1-1
χ6111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1i−i-1ii−i−i-1-1-1-1−i−i−i−iiiii11
χ7111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1−i−iii-1-1−i−i−i−iiiii11-1−ii-1−i−iii1111−i−i−i−iiiii-1-1
χ8111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1−ii-1−i−iii-1-1-1-1iiii−i−i−i−i11
χ9111111111-1-1111111-1111-111111111111-1-111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-1
χ10111111111-1-1111111-1111-111111111111-1-111-1-1-1-1-1-111111111111111-11-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11
χ11111111111-1-1111111-1111-111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1111111-1-1-1-111-1-1111-1
χ12111111111-1-1111111-1111-111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-111-11111-1-11111-1-111-1-1-11
χ13111111111-1-11111-1-1-1111-11111-1-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i1-11−ii1−i−iii11-1-1ii−i−i−i−iii-11
χ14111111111-1-11111-1-1-1111-11111-1-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i-111−ii1−i−iii-1-111−i−iiiii−i−i1-1
χ15111111111-1-11111-1-1-1111-11111-1-1-1-1-1-1-1-1-111-1-1-1-111−i−iii-1-1−i−i−i−iiiii1-11i−i1ii−i−i11-1-1−i−iiiii−i−i-11
χ16111111111-1-11111-1-1-1111-11111-1-1-1-1-1-1-1-1-111-1-1-1-111−i−iii-1-1−i−i−i−iiiii-111i−i1ii−i−i-1-111ii−i−i−i−iii1-1
χ1722222-1-1-1-1222-1-1222-1222-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-100-122-1-1-1-1-100000000000000
χ1822222-1-1-1-1222-1-1222-1222-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-122-2-2-2-2-1-11111111100-1-2-2-1111100000000000000
χ1922222-1-1-1-1222-1-12-2-2-1222-1-1-1-1-1-2-2-2111122-1-1-1-1-1-1-2-22i2i−2i−2i11−i−i−i−iiiii0012i−2i1−i−iii00000000000000
χ2022222-1-1-1-1222-1-12-2-2-1222-1-1-1-1-1-2-2-2111122-1-1-1-1-1-1-2-2−2i−2i2i2i11iiii−i−i−i−i001−2i2i1ii−i−i00000000000000
χ2122222-1-1-1-1-2-22-1-122212221-1-1-1-1222-1-1-1-1-2-2-1-11111-2-22222-1-1-1-1-1-1-1-1-1-1001-2-21111100000000000000
χ2222222-1-1-1-1-2-22-1-122212221-1-1-1-1222-1-1-1-1-2-2-1-11111-2-2-2-2-2-2-1-111111111001221-1-1-1-100000000000000
χ2322222-1-1-1-1-2-22-1-12-2-212221-1-1-1-1-2-2-21111-2-2-1-11111222i2i−2i−2i11−i−i−i−iiiii00-1−2i2i-1ii−i−i00000000000000
χ2422222-1-1-1-1-2-22-1-12-2-212221-1-1-1-1-2-2-21111-2-2-1-1111122−2i−2i2i2i11iiii−i−i−i−i00-12i−2i-1−i−iii00000000000000
χ25222-2-222222-22-2-222222-2-2-22222-2-2222222-2-2-222-2-2-220000-2-20000000000-2002000000000000000000
χ26222-2-222222-22-2-22-2-222-2-2-2222222-2-2-2-2-22-2-2-222-2-22-20000220000000000200-2000000000000000000
χ27222-2-22222-222-2-2222-22-2-222222-2-222222-22-2-2-2-2222-20000-2-20000000000200-2000000000000000000
χ28222-2-22222-222-2-22-2-2-22-2-22222222-2-2-2-2-2-22-2-2-2-222-220000220000000000-2002000000000000000000
χ29222-2-2-1-1-1-12-2211222-12-2-21-1-1-1-1-2-22-1-1-1-12-211-1-111-22000011−i3−i3i3i3−i3−i3i3i300100-1−i3i3−i3i300000000000000
χ30222-2-2-1-1-1-12-2211222-12-2-21-1-1-1-1-2-22-1-1-1-12-211-1-111-22000011i3i3−i3−i3i3i3−i3−i300100-1i3−i3i3−i300000000000000
χ31222-2-2-1-1-1-12-22112-2-2-12-2-21-1-1-1-122-211112-211-1-1112-20000-1-133−3−3−3−33300-10013−3−3300000000000000
χ32222-2-2-1-1-1-12-22112-2-2-12-2-21-1-1-1-122-211112-211-1-1112-20000-1-1−3−33333−3−300-1001−333−300000000000000
χ33222-2-2-1-1-1-1-2221122212-2-2-1-1-1-1-1-2-22-1-1-1-1-221111-1-12-2000011−i3−i3i3i3−i3−i3i3i300-1001i3−i3i3−i300000000000000
χ34222-2-2-1-1-1-1-2221122212-2-2-1-1-1-1-1-2-22-1-1-1-1-221111-1-12-2000011i3i3−i3−i3i3i3−i3−i300-1001−i3i3−i3i300000000000000
χ35222-2-2-1-1-1-1-222112-2-212-2-2-1-1-1-1-122-21111-221111-1-1-220000-1-133−3−3−3−33300100-1−333−300000000000000
χ36222-2-2-1-1-1-1-222112-2-212-2-2-1-1-1-1-122-21111-221111-1-1-220000-1-1−3−33333−3−300100-13−3−3300000000000000
χ3722-22-22-2-220022-22220-22-202-2-222-2-222-2-2002-200000000002-200000000000000000000002-2002-20000
χ3822-22-22-2-220022-22220-22-202-2-222-2-222-2-2002-200000000002-20000000000000000000000-2200-220000
χ3922-22-22-2-220022-22-2-20-22-202-2-22-222-2-222002-20000000000-2200000000000000000000002i−2i00−2i2i0000
χ4022-22-22-2-220022-22-2-20-22-202-2-22-222-2-222002-20000000000-220000000000000000000000−2i2i002i−2i0000
χ4122-2-222-2-22002-222220-2-2202-2-22-22-222-2-200-220000000000-220000000000000000000000002-2002-200
χ4222-2-222-2-22002-222220-2-2202-2-22-22-222-2-200-220000000000-22000000000000000000000000-2200-2200
χ4322-2-222-2-22002-222-2-20-2-2202-2-222-22-2-22200-2200000000002-20000000000000000000000002i−2i00−2i2i00
χ4422-2-222-2-22002-222-2-20-2-2202-2-222-22-2-22200-2200000000002-2000000000000000000000000−2i2i002i−2i00
χ4544444444444-144-1004-1-1-14-1-1-1-10000000-1-1-1-1-1-1-1-100000000000000004400000000-1-1-1-10000000000
χ4644444444444-144-1004-1-1-14-1-1-1-10000000-1-1-1-1-1-1-1-10000000000000000-4-40000000011110000000000
χ47444444444-4-4-144-100-4-1-1-1-4-1-1-1-1000000011-1-1111100000000000000004-400000000-1-1110000000000
χ48444444444-4-4-144-100-4-1-1-1-4-1-1-1-1000000011-1-111110000000000000000-440000000011-1-10000000000
χ49444-4-444444-4-1-4-4-1004-111-4-1-1-1-10000000-1111-1-11100000000000000000000000000−i5i5−i5i50000000000
χ50444-4-444444-4-1-4-4-1004-111-4-1-1-1-10000000-1111-1-11100000000000000000000000000i5−i5i5−i50000000000
χ51444-4-44444-44-1-4-4-100-4-1114-1-1-1-100000001-11111-1-100000000000000000000000000−i5i5i5−i50000000000
χ52444-4-44444-44-1-4-4-100-4-1114-1-1-1-100000001-11111-1-100000000000000000000000000i5−i5−i5i50000000000
χ5344-44-4-222-2004-224440-44-40-222-24-4-4-2-22200-220000000000-2200000000000000000000000000000000
χ5444-44-4-222-2004-224-4-40-44-40-222-2-44422-2-200-2200000000002-200000000000000000000000000000000
χ5544-4-44-222-20042-24440-4-440-222-2-44-4-2-222002-200000000002-200000000000000000000000000000000
χ5644-4-44-222-20042-24-4-40-4-440-222-24-4422-2-2002-20000000000-2200000000000000000000000000000000
χ574-4000400-400400-44i−4i00000400-40004i−4i0000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000000000000000000000000
χ584-4000400-400400-44i−4i00000400-40004i−4i000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000000000000
χ594-4000400-400400-4−4i4i00000400-4000−4i4i000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000000000000
χ604-4000400-400400-4−4i4i00000400-4000−4i4i0000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000000000000000000000000
χ614-4000-2−2i32i3200400-44i−4i00000-2−2i32i32000−2i2i23−2300000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900−2ζ7−2ζ31−2ζ79−2ζ1032ζ7+2ζ31+2ζ79+2ζ103−2ζ23−2ζ47−2ζ71−2ζ1192ζ23+2ζ47+2ζ71+2ζ1192ζ13+2ζ37+2ζ61+2ζ109−2ζ13−2ζ37−2ζ61−2ζ1092ζ29+2ζ53+2ζ77+2ζ101−2ζ29−2ζ53−2ζ77−2ζ101000000000000000000000000
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χ674-4000-22i3−2i3200400-4−4i4i00000-22i3−2i320002i−2i23−230000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119002ζ29+2ζ53+2ζ77+2ζ101−2ζ29−2ζ53−2ζ77−2ζ1012ζ13+2ζ37+2ζ61+2ζ109−2ζ13−2ζ37−2ζ61−2ζ109−2ζ23−2ζ47−2ζ71−2ζ1192ζ23+2ζ47+2ζ71+2ζ119−2ζ7−2ζ31−2ζ79−2ζ1032ζ7+2ζ31+2ζ79+2ζ103000000000000000000000000
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χ7088888-4-4-4-4-8-8-2-4-4-2004-2-2-24111100000002211-1-1-1-10000000000000000000000000000000000000000
χ71888-8-8-4-4-4-48-8-244-200-4-222411110000000-22-1-111-1-10000000000000000000000000000000000000000
χ72888-8-8-4-4-4-4-88-244-2004-222-4111100000002-2-1-1-1-1110000000000000000000000000000000000000000
χ7388-88-88-8-8800-28-8-20002-220-222-2000000000-2200000000000000000000000000000000000000000000
χ7488-88-8-444-400-2-44-20002-2201-1-110000000001-1−i15i15−i15i150000000000000000000000000000000000000000
χ7588-88-8-444-400-2-44-20002-2201-1-110000000001-1i15−i15i15−i150000000000000000000000000000000000000000
χ7688-8-888-8-8800-2-88-200022-20-222-20000000002-200000000000000000000000000000000000000000000
χ7788-8-88-444-400-24-4-200022-201-1-11000000000-11−i15i15i15−i150000000000000000000000000000000000000000
χ7888-8-88-444-400-24-4-200022-201-1-11000000000-11i15−i15−i15i150000000000000000000000000000000000000000
χ7916-160001600-1600-40040000000-40040000000000000000000000000000000000000000000000000000000
χ8016-16000-8−8i38i3800-4004000000022i3−2i3-20000000000000000000000000000000000000000000000000000000
χ8116-16000-88i3−8i3800-400400000002−2i32i3-20000000000000000000000000000000000000000000000000000000

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