Finite Group Databasebeta

← Group #13022394

Character table — Group #13022394

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444444444444444448888888888888888888888888888101010101010101010101010202020202020202020202020202020202020404040404040404040404040
order12222222222244444451010101010101010101010101010104444202020202020202020202020202020202020202020202020444444444444448888888888888888444488888888
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
χ9111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ12111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ13111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ17111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-111-1-1i−i11-1-1ii−i−iii−i−i11-1-1i−i1-1i−i1-11-1i−i
χ18111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-111-1-1i−i-1-111−i−iii−i−iii-1-111i−i1-1−ii-11-11−ii
χ19111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-1-111−iiii−i−i-1-11111-1-1−i−iii−ii-11-11i−i−ii1-1
χ20111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-1-111−ii−i−iii11-1-1-1-111ii−i−i−ii-111-1−iii−i-11
χ21111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1−ii-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-111-1-1i−i11-1-1ii−i−iii−i−i11-1-1−ii-11−ii-11-11−ii
χ22111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1−ii-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-111-1-1i−i-1-111−i−iii−i−iii-1-111−ii-11i−i1-11-1i−i
χ23111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1−ii-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-111-1-111−iiii−i−i-1-11111-1-1−i−iiii−i1-11-1−iii−i-11
χ24111-1-1-1-1111-1-1ii−i−ii−i1111111-1-1-1-1-1-11-1-1−ii-11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-111-1-111−ii−i−iii11-1-1-1-111ii−i−ii−i1-1-11i−i−ii1-1
χ25111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1i−i-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-111-1-111i−iii−i−i11-1-1-1-111−i−iii−ii1-1-11−iii−i1-1
χ26111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1i−i-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-111-1-111i−i−i−iii-1-11111-1-1ii−i−i−ii1-11-1i−i−ii-11
χ27111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1i−i-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-111-1-1−ii11-1-1−i−iii−i−iii11-1-1i−i-11i−i-11-11i−i
χ28111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1i−i-11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-111-1-1−ii-1-111ii−i−iii−i−i-1-111i−i-11−ii1-11-1−ii
χ29111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1−ii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-1-111i−iii−i−i11-1-1-1-111−i−iiii−i-111-1i−i−ii-11
χ30111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1−ii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-1-111i−i−i−iii-1-11111-1-1ii−i−ii−i-11-11−iii−i1-1
χ31111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1−ii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-111-1-1−ii11-1-1−i−iii−i−iii11-1-1−ii1-1−ii1-11-1−ii
χ32111-1-1-1-1111-1-1−i−iii−ii1111111-1-1-1-1-1-11-1-1−ii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-111-1-1−ii-1-111ii−i−iii−i−i-1-111−ii1-1i−i-11-11i−i
χ3322222222-2-2-2-22222-2-2222-2-2-2-222-2-2-2-2222000022-2-222-2-2000000000000000022222-22-22-22-2-2-20000000000000000000000000000
χ3422222222-2-2-2-22222-2-2222-2-2-2-222-2-2-2-2222000022-2-222-2-20000000000000000-2-2-2-2-22-22-22-22220000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-22220000-2-222-2-22200000000000000002222-22-22-22-22-2-20000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-22220000-2-222-2-2220000000000000000-2-2-2-22-22-22-22-2220000000000000000000000000000
χ37222-2-2-2-22-2-2222i2i−2i−2i−2i2i222-2-2-2-2-2-222222-2-200002i2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i2-2-222-2-22−2i2i0000000000000000000000000000
χ38222-2-2-2-22-2-2222i2i−2i−2i−2i2i222-2-2-2-2-2-222222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000−2i−2i2i2i-222-2-222-22i−2i0000000000000000000000000000
χ39222-2-2-2-22-2-222−2i−2i2i2i2i−2i222-2-2-2-2-2-222222-2-20000−2i−2i2i2i2i2i−2i−2i00000000000000002i2i−2i−2i-222-2-222-2−2i2i0000000000000000000000000000
χ40222-2-2-2-22-2-222−2i−2i2i2i2i−2i222-2-2-2-2-2-222222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i2-2-222-2-222i−2i0000000000000000000000000000
χ412-2-22-2-2222-22-20000002-2-222-2-22-222-2-222-20000000000000000000000000000000022-22-2-22-2002i−2i2i−2i000000002i−2i2i−2i000000000000
χ422-2-22-2-2222-22-20000002-2-222-2-22-222-2-222-20000000000000000000000000000000022-22-2-22-200−2i2i−2i2i00000000−2i2i−2i2i000000000000
χ432-2-22-2-2222-22-20000002-2-222-2-22-222-2-222-200000000000000000000000000000000-2-22-222-22002-22-200000000-22-22000000000000
χ442-2-22-2-2222-22-20000002-2-222-2-22-222-2-222-200000000000000000000000000000000-2-22-222-2200-22-22000000002-22-2000000000000
χ452-2-22-2-222-22-220000002-2-2-2-2222-2-2-22222-2000000000000000000000000000000002-2-2-2-22220000002-22-22-22-20000000000000000
χ462-2-22-2-222-22-220000002-2-2-2-2222-2-2-22222-2000000000000000000000000000000002-2-2-2-2222000000-22-22-22-220000000000000000
χ472-2-22-2-222-22-220000002-2-2-2-2222-2-2-22222-200000000000000000000000000000000-22222-2-2-20000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ482-2-22-2-222-22-220000002-2-2-2-2222-2-2-22222-200000000000000000000000000000000-22222-2-2-2000000−2i2i−2i2i2i−2i2i−2i0000000000000000
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χ502-2-2-222-222-2-220000002-2-222-2-2-22-2-2222-2200000000000000000000000000000000222-2-2-2-2200−2i2i2i−2i00000000−2i2i2i−2i000000000000
χ512-2-2-222-222-2-220000002-2-222-2-2-22-2-2222-2200000000000000000000000000000000-2-2-22222-2002-2-2200000000-222-2000000000000
χ522-2-2-222-222-2-220000002-2-222-2-2-22-2-2222-2200000000000000000000000000000000-2-2-22222-200-222-2000000002-2-22000000000000
χ532-2-2-222-22-222-20000002-2-2-2-222-2222-2-22-22000000000000000000000000000000002-222-22-2-20000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ542-2-2-222-22-222-20000002-2-2-2-222-2222-2-22-22000000000000000000000000000000002-222-22-2-2000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ552-2-2-222-22-222-20000002-2-2-2-222-2222-2-22-2200000000000000000000000000000000-22-2-22-2220000002-2-22-222-20000000000000000
χ562-2-2-222-22-222-20000002-2-2-2-222-2222-2-22-2200000000000000000000000000000000-22-2-22-222000000-222-22-2-220000000000000000
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
χ59444444444444-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-4-411111111-1-1-1-1-1-1-1-111111111000000000000000000000000000000000000000000
χ60444444444444-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4441111111111111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
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χ6344444444-4-4-4-4-4-4-4-444-1-1-11111-1-11111-1-1-1000011-1-111-1-155−5−555−5−5−5−555−5−555000000000000000000000000000000000000000000
χ6444444444-4-4-4-4-4-4-4-444-1-1-11111-1-11111-1-1-1000011-1-111-1-1−5−555−5−55555−5−555−5−5000000000000000000000000000000000000000000
χ65444-4-4-4-4444-4-44i4i−4i−4i4i−4i-1-1-1-1-1-1-1111111-1114i−4i4-4−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111000000000000000000000000000000000000000000
χ66444-4-4-4-4444-4-44i4i−4i−4i4i−4i-1-1-1-1-1-1-1111111-111−4i4i-44−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1000000000000000000000000000000000000000000
χ67444-4-4-4-4444-4-4−4i−4i4i4i−4i4i-1-1-1-1-1-1-1111111-1114i−4i-44iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1000000000000000000000000000000000000000000
χ68444-4-4-4-4444-4-4−4i−4i4i4i−4i4i-1-1-1-1-1-1-1111111-111−4i4i4-4iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111000000000000000000000000000000000000000000
χ69444-4-4-4-44-4-4444i4i−4i−4i−4i4i-1-1-1111111-1-1-1-1-1110000−i−iiiii−i−ii5i5−i5−i5−i5−i5i5i555−5−5−5−555000000000000000000000000000000000000000000
χ70444-4-4-4-44-4-4444i4i−4i−4i−4i4i-1-1-1111111-1-1-1-1-1110000−i−iiiii−i−i−i5−i5i5i5i5i5−i5−i5−5−55555−5−5000000000000000000000000000000000000000000
χ71444-4-4-4-44-4-444−4i−4i4i4i4i−4i-1-1-1111111-1-1-1-1-1110000ii−i−i−i−iiii5i5−i5−i5−i5−i5i5i5−5−55555−5−5000000000000000000000000000000000000000000
χ72444-4-4-4-44-4-444−4i−4i4i4i4i−4i-1-1-1111111-1-1-1-1-1110000ii−i−i−i−iii−i5−i5i5i5i5i5−i5−i555−5−5−5−555000000000000000000000000000000000000000000
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χ7544-444-4-4-400004-44-400-1-115−55−5-115−55−511-10000-115−5-115−5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19000000000000000000000000000000000000000000
χ7644-444-4-4-400004-44-400-1-11−55−55-11−55−5511-10000-11−55-11−55ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19000000000000000000000000000000000000000000
χ7744-444-4-4-400004-44-400-1-11−55−55-11−55−5511-10000-11−55-11−55−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19000000000000000000000000000000000000000000
χ7844-444-4-4-40000-44-440044-400004-40000-4-440000-4400-44000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.