Finite Group Databasebeta

← Group #13017185

Character table — Group #13017185

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222444444444555588888888101010101010101010101010101010101616161616161616162020202020202020202020202020203232404040404040404040404040
order12224444458888101010444444882020202022448888888888882040404040404040404444444448888882020248888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-1-1-111111111-1-1-1-1iiiiii−i−i−i−i−i−i111111111-1iiii−i−i−i−i-1-1-1-1i−i11-1-1-1-1ii−i−iii−i−i
χ611111111111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−iiiiiii111111111-1−i−i−i−iiiii-1-1-1-1−ii11-1-1-1-1−i−iii−i−iii
χ711111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i11111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1i−i-1-11111−i−iii−i−iii
χ811111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii11111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−ii-1-11111ii−i−iii−i−i
χ91111111111-1-1-1-1111111111-1-1111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ101111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ111111111111-1-1-1-11111111-1-111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ121111111111-1-1-1-11111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ131111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111i−i11-1-111ii−i−i−i−iii
χ141111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−ii11-1-111−i−iiiii−i−i
χ151111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1iiiiii−i−i−i−i−i−i1-1-1-1-11111-1−i−i−i−iiiii1111i−i-1-111-1-1−i−iiiii−i−i
χ161111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1−i−i−i−i−i−iiiiiii1-1-1-1-11111-1iiii−i−i−i−i1111−ii-1-111-1-1ii−i−i−i−iii
χ171111-1-1-1-111ii−i−i11111111-1i−i-1-1-1-1-1-1-1-11111-1-11111-1-11ii−i−iii−i−i1ii−i−iii−i−iii−i−i-1-11-11-1i−i1-11-1i−ii−i
χ181111-1-1-1-111ii−i−i11111111-1i−i-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111ii−i−iii−i−i1−i−iii−i−iiiii−i−i111-11-1i−i-11-11−ii−ii
χ191111-1-1-1-111ii−i−i1111111-11−ii-1-1-1-1-1-1-1-11111-1-11111-1-11ii−i−i−i−iii1ii−i−iii−i−iii−i−i-1-1-11-11−ii-11-11−ii−ii
χ201111-1-1-1-111ii−i−i1111111-11−ii-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111ii−i−i−i−iii1−i−iii−i−iiiii−i−i11-11-11−ii1-11-1i−ii−i
χ211111-1-1-1-111ii−i−i111-1-1-1-11-1i−i-1-1-1-11111iiii−i−i−i−i−i−iii1ii−i−iii−i−i-1-1-11111-1-1−i−iii−ii1-1-11−iii−i−ii-111-1
χ221111-1-1-1-111ii−i−i111-1-1-1-11-1i−i-1-1-1-11111−i−i−i−iiiiiii−i−i1ii−i−iii−i−i-111-1-1-1-111−i−iiii−i1-1-11−ii−iii−i1-1-11
χ231111-1-1-1-111ii−i−i111-1-1-1-1-11−ii-1-1-1-11111iiii−i−i−i−i−i−iii1ii−i−i−i−iii-1-1-11111-1-1−i−iii−ii-111-1i−i−iii−i1-1-11
χ241111-1-1-1-111ii−i−i111-1-1-1-1-11−ii-1-1-1-11111−i−i−i−iiiiiii−i−i1ii−i−i−i−iii-111-1-1-1-111−i−iiii−i-111-1i−ii−i−ii-111-1
χ251111-1-1-1-111−i−iii11111111-1−ii-1-1-1-1-1-1-1-11111-1-11111-1-11−i−iii−i−iii1−i−iii−i−iii−i−iii-1-11-11-1−ii1-11-1−ii−ii
χ261111-1-1-1-111−i−iii11111111-1−ii-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111−i−iii−i−iii1ii−i−iii−i−i−i−iii111-11-1−ii-11-11i−ii−i
χ271111-1-1-1-111−i−iii1111111-11i−i-1-1-1-1-1-1-1-11111-1-11111-1-11−i−iiiii−i−i1−i−iii−i−iii−i−iii-1-1-11-11i−i-11-11i−ii−i
χ281111-1-1-1-111−i−iii1111111-11i−i-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111−i−iiiii−i−i1ii−i−iii−i−i−i−iii11-11-11i−i1-11-1−ii−ii
χ291111-1-1-1-111−i−iii111-1-1-1-11-1−ii-1-1-1-11111iiii−i−i−i−i−i−iii1−i−iii−i−iii-111-1-1-1-111ii−i−i−ii1-1-11i−ii−i−ii1-1-11
χ301111-1-1-1-111−i−iii111-1-1-1-11-1−ii-1-1-1-11111−i−i−i−iiiiiii−i−i1−i−iii−i−iii-1-1-11111-1-1ii−i−ii−i1-1-11i−i−iii−i-111-1
χ311111-1-1-1-111−i−iii111-1-1-1-1-11i−i-1-1-1-11111iiii−i−i−i−i−i−iii1−i−iiiii−i−i-111-1-1-1-111ii−i−i−ii-111-1−ii−iii−i-111-1
χ321111-1-1-1-111−i−iii111-1-1-1-1-11i−i-1-1-1-11111−i−i−i−iiiiiii−i−i1−i−iiiii−i−i-1-1-11111-1-1ii−i−ii−i-111-1−iii−i−ii1-1-11
χ33222222-2-2-2200002222222000022-2-222-2-222-2-22222-2-222-200000000-2000000000000-2-200000000000000
χ34222222-2-2-2200002222222000022-2-222-2-2-2-222-2-2-2-222-2-2-200000000-20000000000002200000000000000
χ35222222-2-2-220000222-2-2-2-2000022-2-2-2-2222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2000000002000000000000−2i2i00000000000000
χ36222222-2-2-220000222-2-2-2-2000022-2-2-2-222−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-20000000020000000000002i−2i00000000000000
χ372222-2-222-22000022222220000-2-222-2-22222-2-2-2-222-2-2-2-2-200000000-20000000000002200000000000000
χ382222-2-222-22000022222220000-2-222-2-222-2-22222-2-22222-200000000-2000000000000-2-200000000000000
χ392222-2-222-220000222-2-2-2-20000-2-22222-2-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i-20000000020000000000002i−2i00000000000000
χ402222-2-222-220000222-2-2-2-20000-2-22222-2-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i-2000000002000000000000−2i2i00000000000000
χ4122-2-2002i−2i021+i−1−i1−i−1+i-22-222-2-20000002i−2i002i−2i002i−2i2-2002i−2i2-201+i−1−i1−i−1+i000001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ4222-2-2002i−2i021+i−1−i1−i−1+i-22-222-2-20000002i−2i002i−2i00−2i2i-2200−2i2i-2201+i−1−i1−i−1+i00000−1+i1−i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ4322-2-2002i−2i021+i−1−i1−i−1+i-22-2-2-2220000002i−2i00−2i2i002-2−2i2i00-222i−2i01+i−1−i1−i−1+i00000−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i0000000000000000
χ4422-2-2002i−2i021+i−1−i1−i−1+i-22-2-2-2220000002i−2i00−2i2i00-222i−2i002-2−2i2i01+i−1−i1−i−1+i000001+i−1−i−1+i1−i−1−i1+i1−i−1+i−1−i1+i−1+i1−i0000000000000000
χ4522-2-2002i−2i02−1−i1+i−1+i1−i-22-222-2-20000002i−2i002i−2i002i−2i2-2002i−2i2-20−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ4622-2-2002i−2i02−1−i1+i−1+i1−i-22-222-2-20000002i−2i002i−2i00−2i2i-2200−2i2i-220−1−i1+i−1+i1−i000001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ4722-2-2002i−2i02−1−i1+i−1+i1−i-22-2-2-2220000002i−2i00−2i2i002-2−2i2i00-222i−2i0−1−i1+i−1+i1−i000001+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i0000000000000000
χ4822-2-2002i−2i02−1−i1+i−1+i1−i-22-2-2-2220000002i−2i00−2i2i00-222i−2i002-2−2i2i0−1−i1+i−1+i1−i00000−1−i1+i1−i−1+i1+i−1−i−1+i1−i1+i−1−i1−i−1+i0000000000000000
χ4922-2-200−2i2i021−i−1+i1+i−1−i-22-222-2-2000000−2i2i00−2i2i002i−2i-22002i−2i-2201−i−1+i1+i−1−i00000−1−i1+i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ5022-2-200−2i2i021−i−1+i1+i−1−i-22-222-2-2000000−2i2i00−2i2i00−2i2i2-200−2i2i2-201−i−1+i1+i−1−i000001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ5122-2-200−2i2i021−i−1+i1+i−1−i-22-2-2-222000000−2i2i002i−2i002-22i−2i00-22−2i2i01−i−1+i1+i−1−i00000−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i0000000000000000
χ5222-2-200−2i2i021−i−1+i1+i−1−i-22-2-2-222000000−2i2i002i−2i00-22−2i2i002-22i−2i01−i−1+i1+i−1−i000001−i−1+i−1−i1+i−1+i1−i1+i−1−i−1+i1−i−1−i1+i0000000000000000
χ5322-2-200−2i2i02−1+i1−i−1−i1+i-22-222-2-2000000−2i2i00−2i2i002i−2i-22002i−2i-220−1+i1−i−1−i1+i000001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ5422-2-200−2i2i02−1+i1−i−1−i1+i-22-222-2-2000000−2i2i00−2i2i00−2i2i2-200−2i2i2-20−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ5522-2-200−2i2i02−1+i1−i−1−i1+i-22-2-2-222000000−2i2i002i−2i002-22i−2i00-22−2i2i0−1+i1−i−1−i1+i000001−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i0000000000000000
χ5622-2-200−2i2i02−1+i1−i−1−i1+i-22-2-2-222000000−2i2i002i−2i00-22−2i2i002-22i−2i0−1+i1−i−1−i1+i00000−1+i1−i1+i−1−i1−i−1+i−1−i1+i1−i−1+i1+i−1−i0000000000000000
χ57444444444-14444-1-1-100004444-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1000000000000000-1-1000000000000
χ58444444444-14444-1-1-10000-4-4-4-4-1-1-1-10000000000000000-1-1-1-1-1111100000000000000011000000000000
χ59444444444-1-4-4-4-4-1-1-1000044-4-4-1-1-1-10000000000000000-111111111000000000000000-1-1000000000000
χ60444444444-1-4-4-4-4-1-1-10000-4-444-1-1-1-10000000000000000-11111-1-1-1-100000000000000011000000000000
χ614444-4-4-4-44-14i4i−4i−4i-1-1-100004-44i−4i11110000000000000000-1−i−iii−i−iii000000000000000-11000000000000
χ624444-4-4-4-44-14i4i−4i−4i-1-1-10000-44−4i4i11110000000000000000-1−i−iiiii−i−i0000000000000001-1000000000000
χ634444-4-4-4-44-1−4i−4i4i4i-1-1-100004-4−4i4i11110000000000000000-1ii−i−iii−i−i000000000000000-11000000000000
χ644444-4-4-4-44-1−4i−4i4i4i-1-1-10000-444i−4i11110000000000000000-1ii−i−i−i−iii0000000000000001-1000000000000
χ654-44-44i−4i00040000-4-444i−4i4i−4i00004i−4i004-40000000000000000000000000000000000000000000000000000
χ664-44-44i−4i00040000-4-44−4i4i−4i4i00004i−4i00-440000000000000000000000000000000000000000000000000000
χ674-44-4−4i4i00040000-4-444i−4i4i−4i0000−4i4i00-440000000000000000000000000000000000000000000000000000
χ684-44-4−4i4i00040000-4-44−4i4i−4i4i0000−4i4i004-40000000000000000000000000000000000000000000000000000
χ694-4-4400000400004-4-44i−4i−4i4i000000000000−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ370000−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39000000000000000000000000000000000000000000
χ704-4-4400000400004-4-44i−4i−4i4i0000000000004ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ3700004ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ39000000000000000000000000000000000000000000
χ714-4-4400000400004-4-4−4i4i4i−4i000000000000−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ390000−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37000000000000000000000000000000000000000000
χ724-4-4400000400004-4-4−4i4i4i−4i0000000000004ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ3900004ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ37000000000000000000000000000000000000000000
χ73888888-8-8-8-20000-2-2-200000000-2-222000000000000000020000000000000000000000000000000000000
χ748888-8-888-8-20000-2-2-20000000022-2-2000000000000000020000000000000000000000000000000000000
χ7588-8-8008i−8i0-24+4i−4−4i4−4i−4+4i2-220000000000−2i2i00000000000000000−1−i1+i−1+i1−i000000000000000000000000000000000
χ7688-8-8008i−8i0-2−4−4i4+4i−4+4i4−4i2-220000000000−2i2i000000000000000001+i−1−i1−i−1+i000000000000000000000000000000000
χ7788-8-800−8i8i0-24−4i−4+4i4+4i−4−4i2-2200000000002i−2i00000000000000000−1+i1−i−1−i1+i000000000000000000000000000000000
χ7888-8-800−8i8i0-2−4+4i4−4i−4−4i4+4i2-2200000000002i−2i000000000000000001−i−1+i1+i−1−i000000000000000000000000000000000
χ798-88-88i−8i000-2000022-200000000−2i2i00000000000000000000000ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ3800000000000000000000000000000
χ808-88-88i−8i000-2000022-200000000−2i2i00000000000000000000000−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ3800000000000000000000000000000
χ818-88-8−8i8i000-2000022-2000000002i−2i00000000000000000000000ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ3800000000000000000000000000000
χ828-88-8−8i8i000-2000022-2000000002i−2i00000000000000000000000−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ3800000000000000000000000000000
χ8316-16-161600000-40000-444000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.