Finite Group Databasebeta

← Group #13104912

Character table — Group #13104912

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122444444444444444444444444448888888888888888888888888888888888882525252550505050505050505050100100100100100100
order1222442255555510101010101010101010101010101010101010101010101010101010101010101010101010101010101020202020202020202020202044444488888888448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ5111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1
χ6111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−i11−i−iii
χ8111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii11ii−i−i
χ91111-1-11-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-11-1
χ101111-1-11-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-11-11
χ111111-1-11-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii
χ121111-1-11-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i
χ131111-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-11-11
χ141111-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-111-11-1
χ151111-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1−iii−i
χ161111-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1i−i−ii
χ1722-2-22-200222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000222222-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000
χ1822-2-22-200222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000222222-2-2-2-2-2-2−2i2i−2i2i−2i2i00000000000000
χ1922-2-2-2200222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000-2-2-2-2-2-22222222i−2i2i−2i−2i2i00000000000000
χ2022-2-2-2200222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000-2-2-2-2-2-2222222−2i2i−2i2i2i−2i00000000000000
χ212-22-20000222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000002i−2i−2i2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ222-22-20000222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000002i−2i−2i2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ232-22-20000222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000−2i2i2i−2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ242-22-20000222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000−2i2i2i−2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ252-2-220000222222-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000000022-2-20000002i−2i2i−2i000000
χ262-2-220000222222-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000000022-2-2000000−2i2i−2i2i000000
χ272-2-220000222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000-2-2220000002-2-22000000
χ282-2-220000222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000-2-222000000-222-2000000
χ29444444444-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-100000000000000000000
χ3044444444-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-100000000000000000000
χ3144444444-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500000000000000000000
χ3244444444-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5200000000000000000000
χ3344444444-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5200000000000000000000
χ3444444444-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500000000000000000000
χ35444444-4-44-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-4-41111111111-4-411111111114-1-1-1-1-14-1-1-1-1-100000000000000000000
χ36444444-4-4-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-111-4-41111111111-4-411111111-14-1-1-1-1-14-1-1-1-100000000000000000000
χ37444444-4-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+511111−51−5−3+52−3+52−3−52−3−521+51+5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500000000000000000000
χ38444444-4-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−521111−3+52−3+521+51+51−51−5−3−52−3−52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5200000000000000000000
χ39444444-4-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+521111−3−52−3−521−51−51+51+5−3+52−3+52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5200000000000000000000
χ40444444-4-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−511111+51+5−3−52−3−52−3+52−3+521−51−5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500000000000000000000
χ414444-4-44-44-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-4-41111111111-411111-41111100000000000000000000
χ424444-4-44-4-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-111-4-4111111111-411111-4111100000000000000000000
χ434444-4-44-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−511111−51−5−3+52−3+52−3−52−3−521+51+5111−5−3+52−3−521+5111−5−3+52−3−521+500000000000000000000
χ444444-4-44-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+521111−3+52−3+521+51+51−51−5−3−52−3−5211−3+521+51−5−3−5211−3+521+51−5−3−5200000000000000000000
χ454444-4-44-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−521111−3−52−3−521−51−51+51+5−3+52−3+5211−3−521−51+5−3+5211−3−521−51+5−3+5200000000000000000000
χ464444-4-44-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+511111+51+5−3−52−3−52−3+52−3+521−51−5111+5−3−52−3+521−5111+5−3−52−3+521−500000000000000000000
χ474444-4-4-444-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-4-4111111111144-1-1-1-1-1-1-1-1-1-1-411111-41111100000000000000000000
χ484444-4-4-44-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-111-4-411111111-1-144-1-1-1-1-1-1-1-11-411111-4111100000000000000000000
χ494444-4-4-44-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5111−5−3+52−3−521+5111−5−3+52−3−521+500000000000000000000
χ504444-4-4-44-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+5211−3+521+51−5−3−5211−3+521+51−5−3−5200000000000000000000
χ514444-4-4-44-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−5211−3−521−51+5−3+5211−3−521−51+5−3+5200000000000000000000
χ524444-4-4-44-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5111+5−3−52−3+521−5111+5−3−52−3+521−500000000000000000000
χ5344-4-44-4004-1-1-1-1-1-411111-4111114-1-1-1-1-1005−55−55−55−55−5005−55−55−55−55−54-1-1-1-1-1-41111100000000000000000000
χ5444-4-44-4004-1-1-1-1-1-411111-4111114-1-1-1-1-100−55−55−55−55−5500−55−55−55−55−554-1-1-1-1-1-41111100000000000000000000
χ5544-4-44-400-14-1-1-1-11-411111-41111-14-1-1-1-15−5005−5−55−555−55−5005−5−55−555−5-14-1-1-1-11-4111100000000000000000000
χ5644-4-44-400-14-1-1-1-11-411111-41111-14-1-1-1-1−5500−555−55−5−55−5500−555−55−5−55-14-1-1-1-11-4111100000000000000000000
χ5744-4-44-400-1-1−1+53−523+52−1−5111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−55−5−55005+52−5−52−5+525−52005−5−55005+52−5−52−5+525−5200-1-1−1+53−523+52−1−5111−5−3+52−3−521+500000000000000000000
χ5844-4-44-400-1-1−1+53−523+52−1−5111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−5−555−500−5−525+525−52−5+5200−555−500−5−525+525−52−5+5200-1-1−1+53−523+52−1−5111−5−3+52−3−521+500000000000000000000
χ5944-4-44-400-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+525−55−5−5−525+5200005−52−5+525−55−5−5−525+5200005−52−5+52-1-13−52−1−5−1+53+5211−3+521+51−5−3−5200000000000000000000
χ6044-4-44-400-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+52−55−555+52−5−520000−5+525−52−55−555+52−5−520000−5+525−52-1-13−52−1−5−1+53+5211−3+521+51−5−3−5200000000000000000000
χ6144-4-44-400-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−525−55−55−52−5+520000−5−525+525−55−55−52−5+520000−5−525+52-1-13+52−1+5−1−53−5211−3−521−51+5−3+5200000000000000000000
χ6244-4-44-400-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−52−55−55−5+525−5200005+52−5−52−55−55−5+525−5200005+52−5−52-1-13+52−1+5−1−53−5211−3−521−51+5−3+5200000000000000000000
χ6344-4-44-400-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+55−5−5500−5+525−525+52−5−52005−5−5500−5+525−525+52−5−5200-1-1−1−53+523−52−1+5111+5−3−52−3+521−500000000000000000000
χ6444-4-44-400-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+5−555−5005−52−5+52−5−525+5200−555−5005−52−5+52−5−525+5200-1-1−1−53+523−52−1+5111+5−3−52−3+521−500000000000000000000
χ6544-4-4-44004-1-1-1-1-1-411111-4111114-1-1-1-1-1005−55−55−55−55−500−55−55−55−55−55-4111114-1-1-1-1-100000000000000000000
χ6644-4-4-44004-1-1-1-1-1-411111-4111114-1-1-1-1-100−55−55−55−55−55005−55−55−55−55−5-4111114-1-1-1-1-100000000000000000000
χ6744-4-4-4400-14-1-1-1-11-411111-41111-14-1-1-1-15−5005−5−55−555−5−5500−555−55−5−551-41111-14-1-1-1-100000000000000000000
χ6844-4-4-4400-14-1-1-1-11-411111-41111-14-1-1-1-1−5500−555−55−5−555−5005−5−55−555−51-41111-14-1-1-1-100000000000000000000
χ6944-4-4-4400-1-1−1+53−523+52−1−5111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−55−5−55005+52−5−52−5+525−5200−555−500−5−525+525−52−5+5200111−5−3+52−3−521+5-1-1−1+53−523+52−1−500000000000000000000
χ7044-4-4-4400-1-1−1+53−523+52−1−5111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−5−555−500−5−525+525−52−5+52005−5−55005+52−5−52−5+525−5200111−5−3+52−3−521+5-1-1−1+53−523+52−1−500000000000000000000
χ7144-4-4-4400-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+525−55−5−5−525+5200005−52−5+52−55−555+52−5−520000−5+525−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+5200000000000000000000
χ7244-4-4-4400-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+52−55−555+52−5−520000−5+525−525−55−5−5−525+5200005−52−5+5211−3+521+51−5−3−52-1-13−52−1−5−1+53+5200000000000000000000
χ7344-4-4-4400-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−525−55−55−52−5+520000−5−525+52−55−55−5+525−5200005+52−5−5211−3−521−51+5−3+52-1-13+52−1+5−1−53−5200000000000000000000
χ7444-4-4-4400-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−52−55−55−5+525−5200005+52−5−525−55−55−52−5+520000−5−525+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−5200000000000000000000
χ7544-4-4-4400-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+55−5−5500−5+525−525+52−5−5200−555−5005−52−5+52−5−525+5200111+5−3−52−3+521−5-1-1−1−53+523−52−1+500000000000000000000
χ7644-4-4-4400-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+5−555−5005−52−5+52−5−525+52005−5−5500−5+525−525+52−5−5200111+5−3−52−3+521−5-1-1−1−53+523−52−1+500000000000000000000
χ778-88-800008-2-2-2-2-28-2-2-2-2-2-822222-82222200000000000000000000000000000000000000000000000000000000
χ788-88-80000-28-2-2-2-2-28-2-2-2-22-822222-8222200000000000000000000000000000000000000000000000000000000
χ798-88-80000-2-2−2+253−53+5−2−25-2-2−2+253−53+5−2−25222−25−3+5−3−52+25222−25−3+5−3−52+2500000000000000000000000000000000000000000000000000000000
χ808-88-80000-2-23−5−2−25−2+253+5-2-23−5−2−25−2+253+522−3+52+252−25−3−522−3+52+252−25−3−500000000000000000000000000000000000000000000000000000000
χ818-88-80000-2-23+5−2+25−2−253−5-2-23+5−2+25−2−253−522−3−52−252+25−3+522−3−52−252+25−3+500000000000000000000000000000000000000000000000000000000
χ828-88-80000-2-2−2−253+53−5−2+25-2-2−2−253+53−5−2+25222+25−3−5−3+52−25222+25−3−5−3+52−2500000000000000000000000000000000000000000000000000000000
χ838-8-8800008-2-2-2-2-2-8222228-2-2-2-2-2-82222200000000000000000000000000000000000000000000000000000000
χ848-8-880000-28-2-2-2-22-82222-28-2-2-2-22-8222200000000000000000000000000000000000000000000000000000000
χ858-8-880000-2-2−2+253−53+5−2−25222−25−3+5−3−52+25-2-2−2+253−53+5−2−25222−25−3+5−3−52+2500000000000000000000000000000000000000000000000000000000
χ868-8-880000-2-23−5−2−25−2+253+522−3+52+252−25−3−5-2-23−5−2−25−2+253+522−3+52+252−25−3−500000000000000000000000000000000000000000000000000000000
χ878-8-880000-2-23+5−2+25−2−253−522−3−52−252+25−3+5-2-23+5−2+25−2−253−522−3−52−252+25−3+500000000000000000000000000000000000000000000000000000000
χ888-8-880000-2-2−2−253+53−5−2+25222+25−3−5−3+52−25-2-2−2−253+53−5−2+25222+25−3−5−3+52−2500000000000000000000000000000000000000000000000000000000

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