Finite Group Databasebeta

← Group #12131848

Character table — Group #12131848

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size111122222222222222444444444444444444448888888888888888888888888888888888888810101010161616161616161616161616161620202020202040404040404040408080
order1244222444551010202020202244444410101010101020202020202022244410101010101010101010101020202020202020202020202020202020202020204444881010202040404040404040402244444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111111111-111-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111111111-111-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-11111111111111111-11-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111111111111111-11-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ11111111111111111111-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-11111-1-1-1-111-1-11111-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111111111111-111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111111111-1-1-1-1-1-1-1-111-1-111-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-11111111111111-111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-11111-1-111-1-111-1-1-11
χ172222222222−1+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+52−1−52−1−52222222−1+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+52−1−52−1−52−1−52−1−52000022−1+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+52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-22-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-2-2−1+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+52−1−52−1−522222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-222−1+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+520000-2-21−521+521−521+521−521−521+521+521−521−521+521+520000000000000000
χ202222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+520000221−521+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+52−1−52−1−52-2-2-2-22222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-22-2-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−52−1−52−1−52−1−5200002-21−521+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+52−1−52−1−52-2-2-2-22222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-22-2-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-221−521+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+520000-22−1+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-222-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200002-2−1+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+5222222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222222−1−52−1−52−1+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+52000022−1−52−1+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+5222222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-22-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-2-2−1−52−1+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+522222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-222−1−52−1−52−1+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+521−521−521−521−520000-2-21+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+522222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521+521+521−521−521−521−520000221+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+52-2-2-2-22222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-22-2-22-21+521+521−521−52−1−52−1−52−1+52−1+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+5200002-21+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+52-2-2-2-22222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-22-2-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+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+520000-221+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+52-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−520000-22−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-222-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200002-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ332222-2-222-2-2222222222-22-20000-2-2-2-22222-2-2-2-20000002-22-2000000002-22-200000000000000002222000000000000000000-2-22-200000000
χ342222-2-222-2-2222222222-22-20000-2-2-2-22222-2-2-2-20000002-22-2000000002-22-20000000000000000-2-2-2-200000000000000000022-2200000000
χ352222-2-222-2-222222222-22-220000-2-2-2-22222-2-2-2-2000000-22-2200000000-22-2200000000000000002222000000000000000000-2-2-2200000000
χ362222-2-222-2-222222222-22-220000-2-2-2-22222-2-2-2-2000000-22-2200000000-22-220000000000000000-2-2-2-2000000000000000000222-200000000
χ3722-2-2222-2-2-22222-2-2-2-22-2-220000222222-2-2-2-2-2-20000002-22-200000000-22-22000000000000000000000000000000000022-2-200002-2000000
χ3822-2-2222-2-2-22222-2-2-2-22-2-220000222222-2-2-2-2-2-20000002-22-200000000-22-220000000000000000000000000000000000-2-2220000-22000000
χ3922-2-2222-2-2-22222-2-2-2-2-222-20000222222-2-2-2-2-2-2000000-22-22000000002-22-2000000000000000000000000000000000022-2-20000-22000000
χ4022-2-2222-2-2-22222-2-2-2-2-222-20000222222-2-2-2-2-2-2000000-22-22000000002-22-20000000000000000000000000000000000-2-22200002-2000000
χ4122-2-22-2-222-22222-2-2-2-2000000002-22-2-2-2222-22-200200-200000000222200000000-2-2-2-2000000002i2i−2i−2i0000000000000000002i−2i0000002i−2i00
χ4222-2-22-2-222-22222-2-2-2-2000000002-22-2-2-2222-22-200200-200000000222200000000-2-2-2-200000000−2i−2i2i2i000000000000000000−2i2i000000−2i2i00
χ4322-2-22-2-222-22222-2-2-2-2000000002-22-2-2-2222-22-200-200200000000-2-2-2-2000000002222000000002i2i−2i−2i0000000000000000002i−2i000000−2i2i00
χ4422-2-22-2-222-22222-2-2-2-2000000002-22-2-2-2222-22-200-200200000000-2-2-2-200000000222200000000−2i−2i2i2i000000000000000000−2i2i0000002i−2i00
χ4522-2-2-22-22-222222-2-2-2-200000000-22-22-2-222-22-220200-200000222200000000-2-2-2-20000000000002i2i−2i−2i000000000000000000−2i2i00002i−2i0000
χ4622-2-2-22-22-222222-2-2-2-200000000-22-22-2-222-22-220200-200000222200000000-2-2-2-2000000000000−2i−2i2i2i0000000000000000002i−2i0000−2i2i0000
χ4722-2-2-22-22-222222-2-2-2-200000000-22-22-2-222-22-220-200200000-2-2-2-20000000022220000000000002i2i−2i−2i000000000000000000−2i2i0000−2i2i0000
χ4822-2-2-22-22-222222-2-2-2-200000000-22-22-2-222-22-220-200200000-2-2-2-2000000002222000000000000−2i−2i2i2i0000000000000000002i−2i00002i−2i0000
χ4922-2-2-2-22-2222222-2-2-2-222-2-222-2-2-2-2-2-222-2-22222200-200222200000000-2-2-2-20000000022-2-222-2-200000022-2-2000000000000000000000000
χ5022-2-2-2-22-2222222-2-2-2-222-2-2-2-222-2-2-2-222-2-22222-200200222200000000-2-2-2-200000000-2-222-2-222000000-2-222000000000000000000000000
χ5122-2-2-2-22-2222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-22222-200200-2-2-2-20000000022220000000022-2-222-2-2000000-2-222000000000000000000000000
χ5222-2-2-2-22-2222222-2-2-2-2-2-222-2-222-2-2-2-222-2-22222200-200-2-2-2-200000000222200000000-2-222-2-22200000022-2-2000000000000000000000000
χ5322-2-2-2-22-222−1+52−1−52−1+52−1−521−521−521+521+5222-2-222-2-21−521−521+521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52200-200−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+521−521−52−1−52−1−521+521+52000000−1+52−1−521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
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χ1048-88i−8i000000−2+25−2−252−252+25−4ζ11−4ζ194ζ11+4ζ19−4ζ3−4ζ74ζ3+4ζ70000-44−4i4i0000000000000000000000000000000000000000001−5−1+52ζ11+2ζ19−2ζ11−2ζ191+5−1−52ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000
χ1058-88i−8i000000−2−25−2+252+252−25−4ζ3−4ζ74ζ3+4ζ7−4ζ11−4ζ194ζ11+4ζ1900004-44i−4i000000000000000000000000000000000000000000−1−51+5−2ζ3−2ζ72ζ3+2ζ7−1+51−5−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000
χ1068-88i−8i000000−2−25−2+252+252−25−4ζ3−4ζ74ζ3+4ζ7−4ζ11−4ζ194ζ11+4ζ190000-44−4i4i0000000000000000000000000000000000000000001+5−1−52ζ3+2ζ7−2ζ3−2ζ71−5−1+52ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000
χ1078-8−8i8i000000−2+25−2−252−252+254ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ700004-4−4i4i000000000000000000000000000000000000000000−1+51−52ζ11+2ζ19−2ζ11−2ζ19−1−51+52ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000
χ1088-8−8i8i000000−2+25−2−252−252+254ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ70000-444i−4i0000000000000000000000000000000000000000001−5−1+5−2ζ11−2ζ192ζ11+2ζ191+5−1−5−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000000
χ1098-8−8i8i000000−2−25−2+252+252−254ζ3+4ζ7−4ζ3−4ζ74ζ11+4ζ19−4ζ11−4ζ1900004-4−4i4i000000000000000000000000000000000000000000−1−51+52ζ3+2ζ7−2ζ3−2ζ7−1+51−52ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000
χ1108-8−8i8i000000−2−25−2+252+252−254ζ3+4ζ7−4ζ3−4ζ74ζ11+4ζ19−4ζ11−4ζ190000-444i−4i0000000000000000000000000000000000000000001+5−1−5−2ζ3−2ζ72ζ3+2ζ71−5−1+5−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000

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