Finite Group Databasebeta

← Group #12153767

Character table — Group #12153767

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222244444444444444448888888888888888888888888888888888888888161616161616161616161616161620202020404040404040404040408080
order1222224444551010101010104444101010102020202020202020224444881010101010101010202020202020202020202020202020202020202020202020482020202040404040404040404444222444448848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111-1-11-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ9111111111111111111-1-1-1-111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-11111-111-1-1-111-1-11-1
χ10111111111111111111-1-1-1-111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-11
χ11111111111111111111-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-111-1-1-1-1-111-11
χ12111111111111111111-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-111111-1-11-1
χ13111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-11
χ14111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1
χ15111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-11111-1-1-1-111-1-1111-1
χ16111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11
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+52−1−52−1−5222222222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−522222-2-2-2-2−1+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+52-2-21−521−521+521+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+52−1−52−1−52-2-2-2-222221−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−52−1−52-2-2-2-2-2-2-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5222−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52−1−5222-2-222-2-2−1+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52−1−5222-2-2-2-222−1+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+521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−52−1+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+52−1−52−1−52-2-22222-2-21−521−521−521−521+521+521+521+521−521−521+521+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+52−1−52−1−52−1−52−1−52-221−521−521+521+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+52−1−52−1−52-2-222-2-2221−521−521−521−521+521+521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+522-2−1+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+5222222222−1−52−1−52−1−52−1−52−1+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+5222−1−52−1−52−1+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+522222-2-2-2-2−1−52−1−52−1−52−1−52−1+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+521−521−521−521−52-2-21+521+521−521−521+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+52-2-2-2-222221+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−52−1−52−1−52−1+52−1+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+52-2-2-2-2-2-2-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+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+5222-2-222-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2−1−52−1−52−1+52−1+521+521+521−521−521+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+5222-2-2-2-222−1−52−1−52−1−52−1−52−1+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+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+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+52-2-22222-2-21+521+521+521+521−521−521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-221+521+521−521−521+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+52-2-222-2-2221+521+521+521+521−521−521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ33222222-2-2-2-22222222200002222-2-2-2-2-2-2-2-22-200000022-2-222-2-20000000000000000000000000000000000000022-2-202-2000000000
χ34222222-2-2-2-22222222200002222-2-2-2-2-2-2-2-22-200000022-2-222-2-200000000000000000000000000000000000000-2-2220-22000000000
χ35222222-2-2-2-22222222200002222-2-2-2-2-2-2-2-2-22000000-2-222-2-2220000000000000000000000000000000000000022-2-20-22000000000
χ36222222-2-2-2-22222222200002222-2-2-2-2-2-2-2-2-22000000-2-222-2-22200000000000000000000000000000000000000-2-22202-2000000000
χ372222-2-22-2-222222222222-2-2-2-2-2-22-22-22-22-20000000000000000-2-2-2-200002222000000000000000000000000002-22-2200-200000000
χ382222-2-22-2-222222222222-2-2-2-2-2-22-22-22-22-20000000000000000-2-2-2-20000222200000000000000000000000000-22-22-200200000000
χ392222-2-22-2-2222222222-2-222-2-2-2-22-22-22-22-2000000000000000022220000-2-2-2-2000000000000000000000000002-22-2-200200000000
χ402222-2-22-2-2222222222-2-222-2-2-2-22-22-22-22-2000000000000000022220000-2-2-2-200000000000000000000000000-22-22200-200000000
χ412222-2-2-222-2222222220000-2-2-2-2-22-22-22-22002-20000000000000000-2-2-2-20000222200000000000000000000002-2-2200002-2000000
χ422222-2-2-222-2222222220000-2-2-2-2-22-22-22-22002-20000000000000000-2-2-2-2000022220000000000000000000000-222-20000-22000000
χ432222-2-2-222-2222222220000-2-2-2-2-22-22-22-2200-22000000000000000022220000-2-2-2-200000000000000000000002-2-220000-22000000
χ442222-2-2-222-2222222220000-2-2-2-2-22-22-22-2200-22000000000000000022220000-2-2-2-20000000000000000000000-222-200002-2000000
χ4522-2-22-2-2-2222222-2-2-2-22i−2i2i−2i-2-222-22-222-22-200000000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000000000000000000000002i−2i2-200
χ4622-2-22-2-2-2222222-2-2-2-22i−2i2i−2i-2-222-22-222-22-200000000000000002i−2i2i−2i00002i−2i2i−2i000000000000000000000000000000000000−2i2i-2200
χ4722-2-22-2-2-2222222-2-2-2-2−2i2i−2i2i-2-222-22-222-22-20000000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000000000000000002i−2i-2200
χ4822-2-22-2-2-2222222-2-2-2-2−2i2i−2i2i-2-222-22-222-22-20000000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000000000000000000000−2i2i2-200
χ4922-2-2-22-22-222222-2-2-2-22i−2i−2i2i22-2-2-2-2-2-2222200002i−2i2-200000000−2i2i−2i2i00002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000002-22-200000000000000000000
χ5022-2-2-22-22-222222-2-2-2-22i−2i−2i2i22-2-2-2-2-2-222220000−2i2i-2200000000−2i2i−2i2i00002i−2i2i−2i0000−2i−2i2i2i−2i−2i2i2i000000-22-2200000000000000000000
χ5122-2-2-22-22-222222-2-2-2-2−2i2i2i−2i22-2-2-2-2-2-2222200002i−2i-22000000002i−2i2i−2i0000−2i2i−2i2i00002i2i−2i−2i2i2i−2i−2i000000-22-2200000000000000000000
χ5222-2-2-22-22-222222-2-2-2-2−2i2i2i−2i22-2-2-2-2-2-222220000−2i2i2-2000000002i−2i2i−2i0000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i0000002-22-200000000000000000000
χ5322-2-2-22-22-22−1+52−1−52−1+52−1−521−521+521−521+522i−2i−2i2i−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−5200002i−2i2-2ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ700−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
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χ978-88-8000000−2+25−2−252−252+252−252+25−2+25−2−25000000000000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ18000000000000000000000000000000
χ988-88-8000000−2−25−2+252+252−252+252−25−2−25−2+25000000000000000000000000000000000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000000
χ998-88-8000000−2−25−2+252+252−252+252−25−2−25−2+250000000000000000000000000000000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000000
χ1008-8-8800000088-8-888-8-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88000000−2+25−2−252−252+25−2+25−2−252−252+25000000000000000000000000000000000000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000
χ1028-8-88000000−2+25−2−252−252+25−2+25−2−252−252+250000000000000000000000000000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000
χ1038-8-88000000−2−25−2+252+252−25−2−25−2+252+252−250000000000000000000000000000000000000000000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000
χ1048-8-88000000−2−25−2+252+252−25−2−25−2+252+252−25000000000000000000000000000000000000000000000000−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000

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