Finite Group Databasebeta

← Group #13016223

Character table — Group #13016223

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11112222444444444444455558888888888881010101020202020202020202020202020404040401111222244444444444445555888888888888101010102020202020202020202020202040404040
order12222244444445101010101010104444202020202020202020202020224424444444444448888222222444444410101010101010104444202020202020202020202020224424444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ6111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ91111-1-1-1-11ii−i−i111-1-11-1-1111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−iii−i−iii−i−i1-11-11111-1-1-1-11ii−i−i111-1-11-1-1111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−iii−i−iii−i−i1-11-1
χ101111-1-1-1-11ii−i−i111-1-11-1-1111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−i−i−iii−i−iii-11-111111-1-1-1-11ii−i−i111-1-11-1-1111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−i−i−iii−i−iii-11-11
χ111111-1-1-1-11ii−i−i111-1-11-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii11-1-1-1-111−iii−i1111-1-1-1-11ii−i−i111-1-11-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii11-1-1-1-111−iii−i
χ121111-1-1-1-11ii−i−i111-1-11-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii-1-11111-1-1i−i−ii1111-1-1-1-11ii−i−i111-1-11-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii-1-11111-1-1i−i−ii
χ131111-1-1-1-11−i−iii111-1-11-1-1111111-1-1−i−i−i−iiiii-1-1-1-11−i−iiiii−i−iii−i−i-11-111111-1-1-1-11−i−iii111-1-11-1-1111111-1-1−i−i−i−iiiii-1-1-1-11−i−iiiii−i−iii−i−i-11-11
χ141111-1-1-1-11−i−iii111-1-11-1-1111111-1-1−i−i−i−iiiii-1-1-1-11−i−iii−i−iii−i−iii1-11-11111-1-1-1-11−i−iii111-1-11-1-1111111-1-1−i−i−i−iiiii-1-1-1-11−i−iii−i−iii−i−iii1-11-1
χ151111-1-1-1-11−i−iii111-1-11-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i11-1-1-1-111i−i−ii1111-1-1-1-11−i−iii111-1-11-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i11-1-1-1-111i−i−ii
χ161111-1-1-1-11−i−iii111-1-11-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i-1-11111-1-1−iii−i1111-1-1-1-11−i−iii111-1-11-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i-1-11111-1-1−iii−i
χ17222222-2-2-20000222222222222-2-2-2-200000000-2-222-20000000000000000222222-2-2-20000222222222222-2-2-2-200000000-2-222-20000000000000000
χ18222222-2-2-2000022222222-2-2-2-2-2-2-2-20000000022-2-220000000000000000222222-2-2-2000022222222-2-2-2-2-2-2-2-20000000022-2-220000000000000000
χ192222-2-222-20000222-2-22-2-22222-2-2220000000022-2-2-200000000000000002222-2-222-20000222-2-22-2-22222-2-2220000000022-2-2-20000000000000000
χ202222-2-222-20000222-2-22-2-2-2-2-2-2-2-22200000000-2-222200000000000000002222-2-222-20000222-2-22-2-2-2-2-2-2-2-22200000000-2-22220000000000000000
χ2122-2-2002i−2i01+i−1−i1−i−1+i22-200-2002i2i−2i−2i002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2-20001−i−1+i1+i−1−i00000000000022-2-2002i−2i01+i−1−i1−i−1+i22-200-2002i2i−2i−2i002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2-20001−i−1+i1+i−1−i000000000000
χ2222-2-2002i−2i01+i−1−i1−i−1+i22-200-200−2i−2i2i2i002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i-22000−1+i1−i−1−i1+i00000000000022-2-2002i−2i01+i−1−i1−i−1+i22-200-200−2i−2i2i2i002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i-22000−1+i1−i−1−i1+i000000000000
χ2322-2-2002i−2i0−1−i1+i−1+i1−i22-200-2002i2i−2i−2i002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2000−1+i1−i−1−i1+i00000000000022-2-2002i−2i0−1−i1+i−1+i1−i22-200-2002i2i−2i−2i002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2000−1+i1−i−1−i1+i000000000000
χ2422-2-2002i−2i0−1−i1+i−1+i1−i22-200-200−2i−2i2i2i002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i-220001−i−1+i1+i−1−i00000000000022-2-2002i−2i0−1−i1+i−1+i1−i22-200-200−2i−2i2i2i002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i-220001−i−1+i1+i−1−i000000000000
χ2522-2-200−2i2i01−i−1+i1+i−1−i22-200-2002i2i−2i−2i00−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i-22000−1−i1+i−1+i1−i00000000000022-2-200−2i2i01−i−1+i1+i−1−i22-200-2002i2i−2i−2i00−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i-22000−1−i1+i−1+i1−i000000000000
χ2622-2-200−2i2i01−i−1+i1+i−1−i22-200-200−2i−2i2i2i00−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2-20001+i−1−i1−i−1+i00000000000022-2-200−2i2i01−i−1+i1+i−1−i22-200-200−2i−2i2i2i00−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2-20001+i−1−i1−i−1+i000000000000
χ2722-2-200−2i2i0−1+i1−i−1−i1+i22-200-2002i2i−2i−2i00−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i-220001+i−1−i1−i−1+i00000000000022-2-200−2i2i0−1+i1−i−1−i1+i22-200-2002i2i−2i−2i00−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i-220001+i−1−i1−i−1+i000000000000
χ2822-2-200−2i2i0−1+i1−i−1−i1+i22-200-200−2i−2i2i2i00−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2000−1−i1+i−1+i1−i00000000000022-2-200−2i2i0−1+i1−i−1−i1+i22-200-200−2i−2i2i2i00−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2000−1−i1+i−1+i1−i000000000000
χ292-22-22-200000002-22-2-2-2222i−2i2i−2i000000000000002i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002-22-22-200000002-22-2-2-2222i−2i2i−2i000000000000002i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302-22-22-200000002-22-2-2-2222i−2i2i−2i000000000000002i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002-22-22-200000002-22-2-2-2222i−2i2i−2i000000000000002i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312-22-22-200000002-22-2-2-222−2i2i−2i2i00000000000000−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002-22-22-200000002-22-2-2-222−2i2i−2i2i00000000000000−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322-22-22-200000002-22-2-2-222−2i2i−2i2i00000000000000−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002-22-22-200000002-22-2-2-222−2i2i−2i2i00000000000000−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332-22-2-2200000002-2222-2-2-22i−2i2i−2i00000000000000−2i2i000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00002-22-2-2200000002-2222-2-2-22i−2i2i−2i00000000000000−2i2i000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ342-22-2-2200000002-2222-2-2-22i−2i2i−2i00000000000000−2i2i00000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00002-22-2-2200000002-2222-2-2-22i−2i2i−2i00000000000000−2i2i00000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ352-22-2-2200000002-2222-2-2-2−2i2i−2i2i000000000000002i−2i000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00002-22-2-2200000002-2222-2-2-2−2i2i−2i2i000000000000002i−2i000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ362-22-2-2200000002-2222-2-2-2−2i2i−2i2i000000000000002i−2i00000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00002-22-2-2200000002-2222-2-2-2−2i2i−2i2i000000000000002i−2i00000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ374444444444444-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000004444444444444-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ38444444444-4-4-4-4-1-1-1-1-1-1-1-10000-1-1-1-111111111000000000000000000000444444444-4-4-4-4-1-1-1-1-1-1-1-10000-1-1-1-111111111000000000000000000000
χ39444444-4-4-40000-1-1-1-1-1-1-1-1000011115−55−55−55−5000000000000000000000444444-4-4-40000-1-1-1-1-1-1-1-1000011115−55−55−55−5000000000000000000000
χ40444444-4-4-40000-1-1-1-1-1-1-1-100001111−55−55−55−55000000000000000000000444444-4-4-40000-1-1-1-1-1-1-1-100001111−55−55−55−55000000000000000000000
χ414444-4-444-40000-1-1-111-111000011-1-1i5−i5i5−i5−i5i5−i5i50000000000000000000004444-4-444-40000-1-1-111-111000011-1-1i5−i5i5−i5−i5i5−i5i5000000000000000000000
χ424444-4-444-40000-1-1-111-111000011-1-1−i5i5−i5i5i5−i5i5−i50000000000000000000004444-4-444-40000-1-1-111-111000011-1-1−i5i5−i5i5i5−i5i5−i5000000000000000000000
χ434444-4-4-4-444i4i−4i−4i-1-1-111-1110000-1-111−i−i−i−iiiii0000000000000000000004444-4-4-4-444i4i−4i−4i-1-1-111-1110000-1-111−i−i−i−iiiii000000000000000000000
χ444444-4-4-4-44−4i−4i4i4i-1-1-111-1110000-1-111iiii−i−i−i−i0000000000000000000004444-4-4-4-44−4i−4i4i4i-1-1-111-1110000-1-111iiii−i−i−i−i000000000000000000000
χ4544-4-4004i−4i02+2i−2−2i2−2i−2+2i-1-115−515−50000i5−i5−ii−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ1900000000000000000000044-4-4004i−4i02+2i−2−2i2−2i−2+2i-1-115−515−50000i5−i5−ii−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19000000000000000000000
χ4644-4-4004i−4i02+2i−2−2i2−2i−2+2i-1-11−551−550000−i5i5−ii−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ1400000000000000000000044-4-4004i−4i02+2i−2−2i2−2i−2+2i-1-11−551−550000−i5i5−ii−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14000000000000000000000
χ4744-4-4004i−4i0−2−2i2+2i−2+2i2−2i-1-115−515−50000i5−i5−iiζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ1900000000000000000000044-4-4004i−4i0−2−2i2+2i−2+2i2−2i-1-115−515−50000i5−i5−iiζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19000000000000000000000
χ4844-4-4004i−4i0−2−2i2+2i−2+2i2−2i-1-11−551−550000−i5i5−iiζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ1400000000000000000000044-4-4004i−4i0−2−2i2+2i−2+2i2−2i-1-11−551−550000−i5i5−iiζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14000000000000000000000
χ4944-4-400−4i4i02−2i−2+2i2+2i−2−2i-1-115−515−50000−i5i5i−iζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ1900000000000000000000044-4-400−4i4i02−2i−2+2i2+2i−2−2i-1-115−515−50000−i5i5i−iζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19000000000000000000000
χ5044-4-400−4i4i02−2i−2+2i2+2i−2−2i-1-11−551−550000i5−i5i−i−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ1400000000000000000000044-4-400−4i4i02−2i−2+2i2+2i−2−2i-1-11−551−550000i5−i5i−i−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14000000000000000000000
χ5144-4-400−4i4i0−2+2i2−2i−2−2i2+2i-1-115−515−50000−i5i5i−i−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ1900000000000000000000044-4-400−4i4i0−2+2i2−2i−2−2i2+2i-1-115−515−50000−i5i5i−i−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19000000000000000000000
χ5244-4-400−4i4i0−2+2i2−2i−2−2i2+2i-1-11−551−550000i5−i5i−iζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ1400000000000000000000044-4-400−4i4i0−2+2i2−2i−2−2i2+2i-1-11−551−550000i5−i5i−iζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14000000000000000000000
χ534-4-440000000004-4-4004004-4-440000000000000000000000000000000004-4-440000000004-4-4004004-4-44000000000000000000000000000000000
χ544-4-440000000004-4-400400-444-40000000000000000000000000000000004-4-440000000004-4-400400-444-4000000000000000000000000000000000
χ558-88-88-80000000-22-2222-2-200000000000000000000000000000000000008-88-88-80000000-22-2222-2-20000000000000000000000000000000000000
χ568-88-8-880000000-22-2-2-222200000000000000000000000000000000000008-88-8-880000000-22-2-2-22220000000000000000000000000000000000000
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χ1148-88-8-880000000-22-2-2-22220000000000000000000000000000000000000-88-888-800000002-2222-2-2-20000000000000000000000000000000000000
χ1158-8-88000000000-22225−25-2−25250000000000000000000000000000000000000-888-80000000002-2-2−2525225−250000000000000000000000000000000000000
χ1168-8-88000000000-222−2525-225−250000000000000000000000000000000000000-888-80000000002-2-225−252−25250000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.