Finite Group Databasebeta

← Group #13017053

Character table — Group #13017053

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444444444444444448888888888888888888888888888101010101010101010101010202020202020202020202020202020202020404040404040404040404040
order12222222444444444451010101010101020202020202020204444202020202020202020202020202020202020202020202020222244444444448888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
χ81111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ911111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1711-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1811-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-1i−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii-11−ii
χ1911-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−i−iii-1-111−iiii−i−i-1-111−i−iii11-1-1-11−iii−i-11−ii1-1
χ2011-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−i−iii-1-111−ii−i−iii11-1-1ii−i−i-1-111-11−ii−ii1-1i−i-11
χ2111-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i11-1-1i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ2211-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i11-1-1i−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ2311-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-11-11−i−iii-1-111−iiii−i−i-1-111−i−iii11-1-11-1i−i−ii1-1i−i-11
χ2411-1-11-11-1ii−i−iii−i−i1-1111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-11-11−i−iii-1-111−ii−i−iii11-1-1ii−i−i-1-1111-1i−ii−i-11−ii1-1
χ2511-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ2611-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−ii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i-11i−i
χ2711-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i-1-111i−iii−i−i11-1-1−i−iii-1-111-11i−ii−i1-1−ii-11
χ2811-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i-1-111i−i−i−iii-1-111ii−i−i11-1-1-11i−i−ii-11i−i1-1
χ2911-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii11-1-1−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i
χ3011-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii11-1-1−ii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ3111-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i-1-111i−iii−i−i11-1-1−i−iii-1-1111-1−ii−ii-11i−i1-1
χ3211-1-11-11-1−i−iii−i−iii1-1111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i-1-111i−i−i−iii-1-111ii−i−i11-1-11-1−iii−i1-1−ii-11
χ33222222222222-2-2-2-2-2-222222222222222220000-2-2-2-2-2-2-2-2000000000000000022222222-2-2-2-2-2-20000000000000000000000000000
χ34222222222222-2-2-2-2-2-222222222222222220000-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-22222220000000000000000000000000000
χ3522222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-20000-2-2-2-2222200000000000000002222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ3622222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-20000-2-2-2-222220000000000000000-2-2-2-222222222-2-20000000000000000000000000000
χ372222-2-2-2-22-22-200000022-22-22-2-222-2-222-2-2000000000000000000000000000022-2-22-22-20000002−22−22−22−22−22−22−22−2000000000000
χ382222-2-2-2-22-22-200000022-22-22-2-222-2-222-2-2000000000000000000000000000022-2-22-22-2000000−22−22−22−22−22−22−22−22000000000000
χ392222-2-2-2-22-22-200000022-22-22-2-222-2-222-2-20000000000000000000000000000-2-222-22-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402222-2-2-2-22-22-200000022-22-22-2-222-2-222-2-20000000000000000000000000000-2-222-22-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ412222-2-2-2-2-22-2200000022-22-22-2-2-2-222-2-222000000000000000000000000000022-2-2-22-220000002−22−2−22−222−22−2−22−22000000000000
χ422222-2-2-2-2-22-2200000022-22-22-2-2-2-222-2-222000000000000000000000000000022-2-2-22-22000000−22−222−22−2−22−222−22−2000000000000
χ432222-2-2-2-2-22-2200000022-22-22-2-2-2-222-2-2220000000000000000000000000000-2-2222-22-2000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442222-2-2-2-2-22-2200000022-22-22-2-2-2-222-2-2220000000000000000000000000000-2-2222-22-2000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-22-22-22i2i−2i−2i−2i−2i2i2i-22222-2-2-22-22i2i2i2i−2i−2i−2i−2i0000-2-222−2i−2i2i2i00000000000000002-22-22i2i−2i−2i-2-222−2i2i0000000000000000000000000000
χ4622-2-22-22-22i2i−2i−2i−2i−2i2i2i-22222-2-2-22-22i2i2i2i−2i−2i−2i−2i0000-2-222−2i−2i2i2i0000000000000000-22-22−2i−2i2i2i22-2-22i−2i0000000000000000000000000000
χ4722-2-22-22-2−2i−2i2i2i2i2i−2i−2i-22222-2-2-22-2−2i−2i−2i−2i2i2i2i2i0000-2-2222i2i−2i−2i00000000000000002-22-2−2i−2i2i2i-2-2222i−2i0000000000000000000000000000
χ4822-2-22-22-2−2i−2i2i2i2i2i−2i−2i-22222-2-2-22-2−2i−2i−2i−2i2i2i2i2i0000-2-2222i2i−2i−2i0000000000000000-22-222i2i−2i−2i22-2-2−2i2i0000000000000000000000000000
χ4922-2-2-22-222i−2i−2i2i00000022-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000002-2-222i−2i−2i2i0000002−2−22i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ5022-2-2-22-222i−2i−2i2i00000022-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000002-2-222i−2i−2i2i000000−222−2−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ5122-2-2-22-222i−2i−2i2i00000022-2-22-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000-222-2−2i2i2i−2i000000i2−i2−i2i2−222−2−i2i2i2−i22−2−22000000000000
χ5222-2-2-22-222i−2i−2i2i00000022-2-22-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000-222-2−2i2i2i−2i000000−i2i2i2−i22−2−22i2−i2−i2i2−222−2000000000000
χ5322-2-2-22-22−2i2i2i−2i00000022-2-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002-2-22−2i2i2i−2i0000002−2−22−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ5422-2-2-22-22−2i2i2i−2i00000022-2-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002-2-22−2i2i2i−2i000000−222−2i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ5522-2-2-22-22−2i2i2i−2i00000022-2-22-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000-222-22i−2i−2i2i000000i2−i2−i2i22−2−22−i2i2i2−i2−222−2000000000000
χ5622-2-2-22-22−2i2i2i−2i00000022-2-22-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000-222-22i−2i−2i2i000000−i2i2i2−i2−222−2i2−i2−i2i22−2−22000000000000
χ57444444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ58444444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000000000000000
χ59444444444444-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111155−5−555−5−555−5−555−5−5000000000000000000000000000000000000000000
χ60444444444444-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111−5−555−5−555−5−555−5−555000000000000000000000000000000000000000000
χ6144444444-4-4-4-44444-4-4-1-1-1-1-1-1-1-11111111100001111-1-1-1-155−5−555−5−5−5−555−5−555000000000000000000000000000000000000000000
χ6244444444-4-4-4-44444-4-4-1-1-1-1-1-1-1-11111111100001111-1-1-1-1−5−555−5−55555−5−555−5−5000000000000000000000000000000000000000000
χ6344444444-4-4-4-4-4-4-4-444-1-1-1-1-1-1-1-11111111144-4-4-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000000000000000000000000000000000
χ6444444444-4-4-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-4-444-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ6544-4-44-44-44i4i−4i−4i4i4i−4i−4i4-4-1-1-1111-11−i−i−i−iiiii4-44i−4i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii000000000000000000000000000000000000000000
χ6644-4-44-44-44i4i−4i−4i4i4i−4i−4i4-4-1-1-1111-11−i−i−i−iiiii-44−4i4i-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i000000000000000000000000000000000000000000
χ6744-4-44-44-44i4i−4i−4i−4i−4i4i4i-44-1-1-1111-11−i−i−i−iiiii000011-1-1ii−i−i55−5−5−5−555i5i5−i5−i5−i5−i5i5i5000000000000000000000000000000000000000000
χ6844-4-44-44-44i4i−4i−4i−4i−4i4i4i-44-1-1-1111-11−i−i−i−iiiii000011-1-1ii−i−i−5−55555−5−5−i5−i5i5i5i5i5−i5−i5000000000000000000000000000000000000000000
χ6944-4-44-44-4−4i−4i4i4i4i4i−4i−4i-44-1-1-1111-11iiii−i−i−i−i000011-1-1−i−iii55−5−5−5−555−i5−i5i5i5i5i5−i5−i5000000000000000000000000000000000000000000
χ7044-4-44-44-4−4i−4i4i4i4i4i−4i−4i-44-1-1-1111-11iiii−i−i−i−i000011-1-1−i−iii−5−55555−5−5i5i5−i5−i5−i5−i5i5i5000000000000000000000000000000000000000000
χ7144-4-44-44-4−4i−4i4i4i−4i−4i4i4i4-4-1-1-1111-11iiii−i−i−i−i4-4−4i4i-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i000000000000000000000000000000000000000000
χ7244-4-44-44-4−4i−4i4i4i−4i−4i4i4i4-4-1-1-1111-11iiii−i−i−i−i-444i−4i-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000000000000000000000
χ734-44-44-4-4400004i−4i4i−4i004-4-444-44-400000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ744-44-44-4-4400004i−4i4i−4i00-111-1-11-11i5−i5i5−i5i5−i5i5−i500005−55−5−ii−ii−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.