Finite Group Databasebeta

← Group #72226406

Character table — Group #72226406

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172
size111122222244444444444444444444888888888888888888888888888888888888888888888888888888888888888888888888888888888888888825252525404040404040404050505050505080808080808080808080808080808080100100100100200200200200200200200200200200200200200200200200
order124422244422445510101010101020202020202020205510101010101010101010101010101010101010101010101010101010101010101010101010101010101020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202244888888882224444040404040404040404040404040404022444444444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ71111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ81111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ91111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ101111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ121111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ131111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i
χ141111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii
χ151111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ161111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1722222-2-22-2-2000022-2-2-2-2222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-2-2-200000000000000002222-2-20000000022222222-2-2-2-2-2-2-2-20000000000000000222200000000-22-22-2-2000000000000000000000000000000002-22-2
χ1822222-2-22-2-2000022-2-2-2-2222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-2-2-200000000000000002222-2-20000000022222222-2-2-2-2-2-2-2-20000000000000000222200000000-22-22-2-200000000000000000000000000000000-22-22
χ1922222-2-22-2-2000022-2-2-2-2222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-2-2-200000000000000002222-2-20000000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2000000002-22-222000000000000000000000000000000002i−2i−2i2i
χ2022222-2-22-2-2000022-2-2-2-2222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-2-2-200000000000000002222-2-20000000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2000000002-22-22200000000000000000000000000000000−2i2i2i−2i
χ212222-22-2-22-2000022-2-2-2-2222222-2-2-2-222-2-22200000000-2-2-2-22222-2-2-2-2000000000000000022-2-222000000002222-2-2-2-22222-2-2-2-20000000000000000222200000000-2-22-22-200000000000000000000000000002-22-20000
χ222222-22-2-22-2000022-2-2-2-2222222-2-2-2-222-2-22200000000-2-2-2-22222-2-2-2-2000000000000000022-2-222000000002222-2-2-2-22222-2-2-2-20000000000000000222200000000-2-22-22-20000000000000000000000000000-22-220000
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χ252222-2-22-2-220000222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-22222000000000000000022-2-2-2-2000000002222-2-2-2-2-2-2-2-222220000000000000000222200002-22-22-2-2-2-22000022-2-2000022-2-200000000000000000000
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χ272222-2-22-2-220000222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-22222000000000000000022-2-2-2-2000000002222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-200002-2-22-22222-2000022-2-20000-2-22200000000000000000000
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χ2922-2-2222-2-2-222-2-222222222-2-2-2-2-2-2-2-222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-200000000222-2-2-2000000000000000022-2-20000000000000000
χ3022-2-2222-2-2-222-2-222222222-2-2-2-2-2-2-2-222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-2-22220000000000000000-2-2220000000000000000
χ3122-2-2222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222222-2-200000000222-2-2-20000000000000000-2-2220000000000000000
χ3222-2-2222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222222222-2-22200000000-2-2-2222000000000000000022-2-20000000000000000
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χ3522-2-22-2-2-222000022-2-2-2-222-2-2-2-222222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000022-2-22200000000-2-2-2-2-2-2-2-2222222220000000000000000-2-222000000002-222-2-20000000000000000000000002i−2i−2i2i00000000
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χ1698-8−8i8i000000-444i−4i-2-2−252525−25222i−2i2i−2i2i5−2i5−2i52i5-2300001+5−1−51−5−1+51−5−1+51+5−1−5005-5−25255−500−551+51−5−1−5−1+51−4+5-14−51−4−5-14+51−51+5−1+5−1−52-30000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72i−3i−2i3i00−5i5i2i5−2i5−i5i500i5−i5−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−i3ζ3+3ζ7+5ζ11+5ζ19i−3ζ3−3ζ7−5ζ11−5ζ19−i5ζ3+5ζ7+3ζ11+3ζ19i−5ζ3−5ζ7−3ζ11−3ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7000000000000000000000000000000000000000000000000000000
χ1708-8−8i8i000000-444i−4i-2-2−252525−25222i−2i2i−2i2i5−2i5−2i52i5-2300001+5−1−51−5−1+51−5−1+51+5−1−500-5525−25−5500−551−51+5−1+5−1−5−4+514−5-1−4−514+5-11+51−5−1−5−1+52-30000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72i−3i−2i3i005i−5i−2i52i5i5−i500i5−i5−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ73ζ3+3ζ7+5ζ11+5ζ19−i−3ζ3−3ζ7−5ζ11−5ζ19i5ζ3+5ζ7+3ζ11+3ζ19−i−5ζ3−5ζ7−3ζ11−3ζ19i−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19000000000000000000000000000000000000000000000000000000
χ1718-8−8i8i000000-444i−4i-2-2−2525−2525222i−2i2i−2i2i5−2i52i5−2i53-200001+5−1−51−5−1+51+5−1−51−5−1+55-500−55−25255−5001−4−5-14+51+51−5−1−5−1+51−51+5−1+5−1−51−4+5-14−5-320000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−3i2i3i−2i−5i5i00i5−i52i5−2i5−i5i500−i5ζ3+5ζ7+3ζ11+3ζ19i−5ζ3−5ζ7−3ζ11−3ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−i3ζ3+3ζ7+5ζ11+5ζ19i−3ζ3−3ζ7−5ζ11−5ζ19000000000000000000000000000000000000000000000000000000
χ1728-8−8i8i000000-444i−4i-2-2−2525−2525222i−2i2i−2i2i5−2i52i5−2i53-200001+5−1−51−5−1+51+5−1−51−5−1+5-55005−525−255−500−4−514+5-11−51+5−1+5−1−51+51−5−1−5−1+5−4+514−5-1-320000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−3i2i3i−2i5i−5i00−i5i5−2i52i5−i5i5005ζ3+5ζ7+3ζ11+3ζ19−i−5ζ3−5ζ7−3ζ11−3ζ19i−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ193ζ3+3ζ7+5ζ11+5ζ19−i−3ζ3−3ζ7−5ζ11−5ζ19i000000000000000000000000000000000000000000000000000000

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