Finite Group Databasebeta

← Group #14299699

Character table — Group #14299699

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222444444558888888881010101010101016161616161616162020202020202020202020202020202024244040404040404040484848486060606060606060120120
order1223446662251012124466101520203030302241212121210103030303060604466888824242424242424248888121224242424404040408888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i11i−i-1-1ii−i−i1111iiii−i−i−i−i-1-1
χ6111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1i−i-1-1ii−i−i-1-1-1-1−i−i−i−iiiii11
χ7111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii11−ii-1-1−i−iii1111−i−i−i−iiiii-1-1
χ8111111111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-1-1−ii-1-1−i−iii-1-1-1-1iiii−i−i−i−i11
χ9111111111-1-1111111-1-111111111111111-1-1-1-1-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-1
χ10111111111-1-1111111-1-111111111111111-1-1-1-1-1-111-1-111111111111111-11-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11
χ11111111111-1-1111111-1-111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1-1-1-111-1-1111-1
χ12111111111-1-1111111-1-111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-11
χ13111111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−iiiii−i−i−i−i1-1−ii11−i−iii11-1-1ii−i−i−i−iii-11
χ14111111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−iiiii−i−i−i−i-11−ii11−i−iii-1-111−i−iiiii−i−i1-1
χ15111111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iii−i−i−i−iiiii1-1i−i11ii−i−i11-1-1−i−iiiii−i−i-11
χ16111111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iii−i−i−i−iiiii-11i−i11ii−i−i-1-111ii−i−i−i−iii1-1
χ172222-2-22222-222-2-2222-222-2-2222-2-2222222-222-2-2-2-22-2-2-200000000000000002-2000000000000000000
χ182222-2-22222-222-2-2-2-22-222-2-222222-2-2-2-2-22-222-2-2-2-2-22220000000000000000-22000000000000000000
χ192222-2-2222-2222-2-222-2222-2-2222-2-222222-22-2-222-2-2-22-2-20000000000000000-22000000000000000000
χ202222-2-2222-2222-2-2-2-2-2222-2-222222-2-2-2-2-2-22-2-222-2-22-22200000000000000002-2000000000000000000
χ21222-122-1-1-12222-1-122-1-12-122-1-1-1222-1-1-1-122-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-10022-1-1-1-1-1-100000000000000
χ22222-122-1-1-12222-1-122-1-12-122-1-1-1222-1-1-1-122-1-1-1-1-1-122-1-1-2-2-2-21111111100-2-2-1-1111100000000000000
χ23222-122-1-1-12222-1-1-2-2-1-12-122-1-1-1-2-2-2111122-1-1-1-1-1-1-2-2112i2i−2i−2i−i−i−i−iiiii002i−2i11−i−iii00000000000000
χ24222-122-1-1-12222-1-1-2-2-1-12-122-1-1-1-2-2-2111122-1-1-1-1-1-1-2-211−2i−2i2i2iiiii−i−i−i−i00−2i2i11ii−i−i00000000000000
χ25222-122-1-1-1-2-222-1-122112-122-1-1-1222-1-1-1-1-2-21111-1-1-2-2-1-12222-1-1-1-1-1-1-1-100-2-211111100000000000000
χ26222-122-1-1-1-2-222-1-122112-122-1-1-1222-1-1-1-1-2-21111-1-1-2-2-1-1-2-2-2-211111111002211-1-1-1-100000000000000
χ27222-122-1-1-1-2-222-1-1-2-2112-122-1-1-1-2-2-21111-2-21111-1-122112i2i−2i−2i−i−i−i−iiiii00−2i2i-1-1ii−i−i00000000000000
χ28222-122-1-1-1-2-222-1-1-2-2112-122-1-1-1-2-2-21111-2-21111-1-12211−2i−2i2i2iiiii−i−i−i−i002i−2i-1-1−i−iii00000000000000
χ29222-1-2-2-1-1-12-2221122-112-1-2-2-1-1-1-2-22-1-1-1-12-2-1-111112-2110000−i3−i3i3i3−i3−i3i3i30000-11−i3i3−i3i300000000000000
χ30222-1-2-2-1-1-12-2221122-112-1-2-2-1-1-1-2-22-1-1-1-12-2-1-111112-2110000i3i3−i3−i3i3i3−i3−i30000-11i3−i3i3−i300000000000000
χ31222-1-2-2-1-1-12-22211-2-2-112-1-2-2-1-1-122-211112-2-1-11111-22-1-1000033−3−3−3−33300001-13−3−3300000000000000
χ32222-1-2-2-1-1-12-22211-2-2-112-1-2-2-1-1-122-211112-2-1-11111-22-1-10000−3−33333−3−300001-1−333−300000000000000
χ33222-1-2-2-1-1-1-222211221-12-1-2-2-1-1-1-2-22-1-1-1-1-2211-1-111-22110000−i3−i3i3i3−i3−i3i3i300001-1i3−i3i3−i300000000000000
χ34222-1-2-2-1-1-1-222211221-12-1-2-2-1-1-1-2-22-1-1-1-1-2211-1-111-22110000i3i3−i3−i3i3i3−i3−i300001-1−i3i3−i3i300000000000000
χ35222-1-2-2-1-1-1-222211-2-21-12-1-2-2-1-1-122-21111-2211-1-1112-2-1-1000033−3−3−3−3330000-11−333−300000000000000
χ36222-1-2-2-1-1-1-222211-2-21-12-1-2-2-1-1-122-21111-2211-1-1112-2-1-10000−3−33333−3−30000-113−3−3300000000000000
χ3722-222-2-2-2200222-22200-222-2-2-222-2-222-2-20000002-2002-200000000000000000000000000002-2002-200
χ3822-222-2-2-2200222-22200-222-2-2-222-2-222-2-20000002-2002-20000000000000000000000000000-2200-2200
χ3922-222-2-2-2200222-2-2-200-222-2-2-22-222-2-2220000002-200-2200000000000000000000000000002i−2i00−2i2i00
χ4022-222-2-2-2200222-2-2-200-222-2-2-22-222-2-2220000002-200-220000000000000000000000000000−2i2i002i−2i00
χ4122-22-22-2-220022-222200-22-22-2-22-22-222-2-2000000-2200-22000000000000000000000000002-2002-20000
χ4222-22-22-2-220022-222200-22-22-2-22-22-222-2-2000000-2200-2200000000000000000000000000-2200-220000
χ4322-22-22-2-220022-22-2-200-22-22-2-222-22-2-222000000-22002-2000000000000000000000000002i−2i00−2i2i0000
χ4422-22-22-2-220022-22-2-200-22-22-2-222-22-2-222000000-22002-200000000000000000000000000−2i2i002i−2i0000
χ4544444444444-1-1440044-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-100000000000000004400000000-1-1-1-10000000000
χ4644444444444-1-1440044-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-10000000000000000-4-40000000011110000000000
χ47444444444-4-4-1-14400-4-4-1-1-1-1-1-1-10000000111111-1-100000000000000004-400000000-1-1110000000000
χ48444444444-4-4-1-14400-4-4-1-1-1-1-1-1-10000000111111-1-10000000000000000-440000000011-1-10000000000
χ494444-4-44444-4-1-1-4-4004-4-1-111-1-1-10000000-11-1-1111100000000000000000000000000−i5i5−i5i50000000000
χ504444-4-44444-4-1-1-4-4004-4-1-111-1-1-10000000-11-1-1111100000000000000000000000000i5−i5i5−i50000000000
χ514444-4-4444-44-1-1-4-400-44-1-111-1-1-100000001-111-1-11100000000000000000000000000−i5i5i5−i50000000000
χ524444-4-4444-44-1-1-4-400-44-1-111-1-1-100000001-111-1-11100000000000000000000000000i5−i5−i5i50000000000
χ5344-4-24-422-20044-224400-4-24-422-24-4-4-2-222000000-2200-22000000000000000000000000000000000000
χ5444-4-24-422-20044-22-4-400-4-24-422-2-44422-2-2000000-22002-2000000000000000000000000000000000000
χ5544-4-2-4422-200442-24400-4-2-4422-2-44-4-2-2220000002-2002-2000000000000000000000000000000000000
χ5644-4-2-4422-200442-2-4-400-4-2-4422-24-4422-2-20000002-200-22000000000000000000000000000000000000
χ574-4040000-4004-4004i−4i00040000-40004i−4i000000000000002ζ7+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+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000000000000000000000000
χ584-4040000-4004-4004i−4i00040000-40004i−4i00000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+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
χ594-4040000-4004-400−4i4i00040000-4000−4i4i00000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+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
χ604-4040000-4004-400−4i4i00040000-4000−4i4i000000000000002ζ13+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+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000000000000000000000000
χ614-40-200−2i32i32004-4004i−4i000-200−2i32i32000−2i2i23−230000000000002ζ7+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+2ζ109−2ζ7−2ζ31−2ζ79−2ζ1032ζ7+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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χ70888-488-4-4-4-8-8-2-2-4-40044-21-2-2111000000022-1-1-1-1110000000000000000000000000000000000000000
χ71888-4-8-8-4-4-48-8-2-24400-44-21221110000000-2211-1-1-1-10000000000000000000000000000000000000000
χ72888-4-8-8-4-4-4-88-2-244004-4-212211100000002-2-1-111-1-10000000000000000000000000000000000000000
χ7388-888-8-8-8800-2-28-800002-2-2222-20000000000000-220000000000000000000000000000000000000000
χ7488-88-88-8-8800-2-2-8800002-22-222-200000000000002-20000000000000000000000000000000000000000
χ7588-8-48-844-400-2-2-44000021-22-1-11000000000−i15i15−i15i151-10000000000000000000000000000000000000000
χ7688-8-48-844-400-2-2-44000021-22-1-11000000000i15−i15i15−i151-10000000000000000000000000000000000000000
χ7788-8-4-8844-400-2-24-40000212-2-1-11000000000−i15i15i15−i15-110000000000000000000000000000000000000000
χ7888-8-4-8844-400-2-24-40000212-2-1-11000000000i15−i15−i15i15-110000000000000000000000000000000000000000
χ7916-160160000-1600-440000000-4000040000000000000000000000000000000000000000000000000000000
χ8016-160-800−8i38i3800-4400000002002i3−2i3-20000000000000000000000000000000000000000000000000000000
χ8116-160-8008i3−8i3800-440000000200−2i32i3-20000000000000000000000000000000000000000000000000000000

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