Finite Group Databasebeta

← Group #12156337

Character table — Group #12156337

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107
size111122222222222222444444444444444488888888888888888888888888888888888888888810101616161616161616161616161620202040404040404040404040404080
order1222222222551010101010102244101010101010101010101010444444444410101010202020202020202020202020202020202020202020202020202020204442020202020202020202020204444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-11
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1
χ51111111111111111111111111111111111-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1
χ61111111111111111111111111111111111-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ71111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111111111-1-11-1-11-1-11111-1
χ81111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-111-1-1-1-11
χ9111111111111111111-1-1-1-1111111111111111-11-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-111111-11-1-11-111-1-1-1
χ10111111111111111111-1-1-1-1111111111111111-11-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-11-1-1111
χ11111111111111111111-1-1-1-111111111111111-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-111-1
χ12111111111111111111-1-1-1-111111111111111-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-111-1-11
χ13111111111111111111-1-1-1-1111111111111-1-11-11-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111-1-1-11-1-11-1-1-1111
χ14111111111111111111-1-1-1-1111111111111-1-11-11-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1111-111-1111-1-1-1
χ15111111111111111111-1-1-1-1111111111111-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11-1-1111-1-11
χ16111111111111111111-1-1-1-1111111111111-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11111-111-1-1-111-1
χ172222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−522222222222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ182222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ192222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200-21−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ202222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2-2-2-2-22222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ212222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-22-222-2-21−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-22-22-2-2221−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ232222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22-22-2-2-2221−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521+521+521−521−521−521−521+521+521+521+52002−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ242222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2-22-2222-2-21−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ252222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+522222222222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ262222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+5222-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ272222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200-21+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ282222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-2-2-2-2-22222−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ292222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-22-222-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ302222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+5222-22-22-2-2221+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ312222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22-22-2-2-2221+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521−521−521+521+521+521+521−521−521−521−52002−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ322222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-2-22-2222-2-21+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ3322222-2-2-2-222222222222-2-22-2-22-2-22-2-22-2-2000000000022220000000000000000-2-2-2-2000000002200000000000002-2-200-20020000000
χ3422222-2-2-2-222222222222-2-22-2-22-2-22-2-22-2-2000000000022220000000000000000-2-2-2-200000000-2-20000000000000-22200200-20000000
χ3522222-2-2-2-2222222222-2-2222-2-22-2-22-2-22-2-20000000000-2-2-2-200000000000000002222000000002200000000000002-2-200200-20000000
χ3622222-2-2-2-2222222222-2-2222-2-22-2-22-2-22-2-20000000000-2-2-2-20000000000000000222200000000-2-20000000000000-22200-20020000000
χ372222-22-22-2-2222222220000-22-2-22-2-22-2-22-200020-2000000000000000022-2-222-2-2000000000000220000000000000-22-20000200-200000
χ382222-22-22-2-2222222220000-22-2-22-2-22-2-22-200020-2000000000000000022-2-222-2-2000000000000-2-200000000000002-220000-200200000
χ392222-22-22-2-2222222220000-22-2-22-2-22-2-22-2000-2020000000000000000-2-222-2-222000000000000220000000000000-22-20000-200200000
χ402222-22-22-2-2222222220000-22-2-22-2-22-2-22-2000-2020000000000000000-2-222-2-222000000000000-2-200000000000002-220000200-200000
χ412222-2-22-22-2222222220000-2-22-2-22-2-22-2-220020-200000000022-2-222-2-200000000000000000000220000000000000-2-22000200-2000000
χ422222-2-22-22-2222222220000-2-22-2-22-2-22-2-220020-200000000022-2-222-2-200000000000000000000-2-2000000000000022-2000-2002000000
χ432222-2-22-22-2222222220000-2-22-2-22-2-22-2-2200-202000000000-2-222-2-22200000000000000000000220000000000000-2-22000-2002000000
χ442222-2-22-22-2222222220000-2-22-2-22-2-22-2-2200-202000000000-2-222-2-22200000000000000000000-2-2000000000000022-2000200-2000000
χ4522-2-2-222-2-2222-2-2-2-2222-22-2-2-2-2-2-2-222222200000000002-22-200000000000000002-22-200000000000000000000000000000000002i−2i2i−2i0
χ4622-2-2-222-2-2222-2-2-2-2222-22-2-2-2-2-2-2-222222200000000002-22-200000000000000002-22-20000000000000000000000000000000000−2i2i−2i2i0
χ4722-2-2-222-2-2222-2-2-2-222-22-22-2-2-2-2-2-22222220000000000-22-220000000000000000-22-2200000000000000000000000000000000002i−2i−2i2i0
χ4822-2-2-222-2-2222-2-2-2-222-22-22-2-2-2-2-2-22222220000000000-22-220000000000000000-22-220000000000000000000000000000000000−2i2i2i−2i0
χ4922-2-2-2-2-222222-2-2-2-2222-2-22-222-2222-2-22-2-20000002i−2i2i−2i2-22-20000000000000000-22-220000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ5022-2-2-2-2-222222-2-2-2-2222-2-22-222-2222-2-22-2-2000000−2i2i−2i2i2-22-20000000000000000-22-22000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ5122-2-2-2-2-222222-2-2-2-222-222-2-222-2222-2-22-2-20000002i−2i−2i2i-22-2200000000000000002-22-20000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5222-2-2-2-2-222222-2-2-2-222-222-2-222-2222-2-22-2-2000000−2i2i2i−2i-22-2200000000000000002-22-2000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5322-2-2-2-2-2222−1+52−1−521−521−521+521+52−1+52−1−522-2-221−52−1+52−1+521+52−1−52−1−52−1+521−521−52−1−521+521+520000002i−2i2i−2i−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ71−52−1+521+52−1−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ70000000000000000
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χ1028-88-8000000−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000000000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000000
χ1038-88-8000000−2−25−2+252+25−2−252−25−2+252+252−2500000000000000000000000000000000000000000000000000−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000000
χ1048-8-88000000−2+25−2−25−2+252−25−2−252+252−252+2500000000000000004i−4i00000000000000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000
χ1058-8-88000000−2+25−2−25−2+252−25−2−252+252−252+250000000000000000−4i4i000000000000000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000
χ1068-8-88000000−2−25−2+25−2−252+25−2+252−252+252−2500000000000000004i−4i00000000000000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000
χ1078-8-88000000−2−25−2+25−2−252+25−2+252−252+252−250000000000000000−4i4i000000000000000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000

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